Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

In the past few decades, probabilistic interpretations of brain functions have become widespread in cognitive science and neuroscience. In particular, the free energy principle and active inference are increasingly popular theories of cognitive functions that claim to offer a unified understanding of life and cognition within a general mathematical framework derived from information and control theory, and statistical mechanics. However, we argue that if the active inference proposal is to be taken as a general process theory for biological systems, it is necessary to understand how it relates to existing control theoretical approaches routinely used to study and explain biological systems. For example, recently, PID control has been shown to be implemented in simple molecular systems and is becoming a popular mechanistic explanation of behaviours such as chemotaxis in bacteria and amoebae, and robust adaptation in biochemical networks. In this work, we will show how PID controllers can fit a more general theory of life and cognition under the principle of (variational) free energy minimisation when using approximate linear generative models of the world. This more general interpretation provides also a new perspective on traditional problems of PID controllers such as parameter tuning as well as the need to balance performances and robustness conditions of a controller. Specifically, we then show how these problems can be understood in terms of the optimisation of the precisions (inverse variances) modulating different prediction errors in the free energy functional.

In this paper, we focus on variational Bayesian learning deterministic optimization methods for inference in biparametric exponential models where the parameters follow semiparametric regression structures. This combination of data models and algorithms contributes to solving real-world problems and reduces the computation time. This allows both the rapid exploration of many data models and the accurate estimation of the mean and variance functions through the connection between generalized linear models and graph theory. A simulation study was carried out to assess the performance of the deterministic approximation. Finally, herein, we present an application using macroeconomic data to emphasize the benefits of the proposed approach.

The present era of the Internet of Things (IoT) having intelligent functionalities in solving problems pertaining to realtime mission-critical systems has brought an immense revolution in diverse fields including healthcare and navigation systems. However, to the best of our knowledge, the potential of IoT has not been fully exploited yet in the field of the energy sector. We argue that there is an immense need to shift the traditional mission-critical electric power system architecture to IoT-based fully orchestrated architecture in order to increase efficiency, as billions of investment is reserved for the energy sector globally. Since network orchestration deals with auomating the interaction between multiple components involved to execute a particular service, therefore, scheduling the relevant processes within strict deadlines becomes the core pillar of the architecture. The mission-critical systems with urgent task execution often suffer from issues of missing task deadlines. In this study, we present a novel IoT task orchestration architecture for efficient energy management of a nanogrid system that focuses on minimizing the use of nonrenewable energy resources and maximizing the use of renewable energy resources. Moreover, major components of IoT task orchestration such as task mapping and task scheduling are also enhanced using NLP and PSO optimization modules. The proposed task scheduling algorithm incorporates the optimized surplus time, and efficiently executes the energy management-related tasks contemplating to their types. The study utilizes sensors to obtain data from physical IoT devices, including photovoltaic (PV), Energy Storage System (ESS), and diesel generator (DG). The performance of the proposed model is evaluated using data set of nanogrid houses. The outcomes revealed that IoT-task orchestration has played a pivotal role in efficient energy management for nanogrid mission-critical system. Furthermore, the comparison with state-of-the-art scheduling algorithms showed that the task starvation rate is reduced to 16% and 12% when compared with RR and FEF algorithms, respectively.

This paper aims to provide an adaptation of the TL-moments method to censored data. The present study concentrates on Type-I censored data. The idea of using TL-moments with censored data may seem conflicting. But our perspective in that, we may use data censored from one side and trimmed from the other side. This study is applied to estimate the two unknown parameters of the Weibull distribution. The suggested point is compared with Direct L-moments and ML methods. A Monte Carlo simulation study is carried out to compare these method in terms of estimate average, root of mean square error (RMSE) and relative absolute biases (RAB).

Deep behavioral covariates (DBCs) introduced in this perspective form a new class of covariates that have the potential to enhance the performance of predictive models and improve analytics in clinical decision support applications. DBCs can measure how engaged a patient tends to be and how he or she tends to respond to events, and they may be highly predictive of the patient’s outcomes for a planned treatment. DBCs may potentially serve as a standard to measure patient engagement and activation and may form highly efficient mechanisms for improving patient outcomes.

Numerous approaches address over-fitting in neural networks: by imposing a penalty on the parameters of the network (L1, L2, etc); by changing the network stochastically (drop-out, Gaussian noise, etc.); or by transforming the input data (batch normalization, etc.). In contrast, we aim to ensure that a minimum amount of supporting evidence is present when fitting the model parameters to the training data. This, at the single neuron level, is equivalent to ensuring that both sides of the separating hyperplane (for a standard artificial neuron) have a minimum number of data points — noting that these points need not belong to the same class for the inner layers. We firstly benchmark the results of this approach on the standard Fashion-MINST dataset, comparing it to various regularization techniques. Interestingly, we note that by nudging each neuron to divide, at least in part, its input data, the resulting networks make use of each neuron, avoiding a hyperplane completely on one side of its input data (which is equivalent to a constant into the next layers). To illustrate this point, we study the prevalence of saturated nodes throughout training, showing that neurons are activated more frequently and earlier in training when using this regularization approach. A direct consequence of the improved neuron activation is that deep networks are now easier to train. This is crucially important when the network topology is not known a priori and fitting often remains stuck in a suboptimal local minima. We demonstrate this property by training a network of increasing depth (and constant width): most regularization approaches will result in increasingly frequent training failures (over different random seeds) whilst the proposed evidence-based regularization significantly outperforms in its ability to train deep networks.

In Sub-Saharan African Countries such as Nigeria with high prevalence rate, Child HIV/AIDs acquired through Mother-to-Child transmission (MTCT) can be largely prevented by using a well-established prevention programme and scheme. This study examined factors that can enhanced Prevention of Mother-to-Child transmission (PMTCT) in Nasarawa State. To achieve this, structured questionnaire were used to collect data from one hundred and sixteen (116) women attending two (2) primary facilities and two (2) secondary facilities in the State. This study utilized methods of Poisson Regression, Negative Binomial Regression and Logistic Regression Analyses. Results revealed that women with at least a secondary school education, women with husband in military and women with perceived confidentiality of their HIV status significantly enhanced PMTCT of HIV in Nasarawa State while significant proportion of the women attest to the fact that drugs are available in the facilities (p-value=0.0000<0.05) . Other factors include mother income level, willingness to continue with PMTCT programme and women in support group can also enhanced PMTCT though they are not significant. This study recommends that the factors identified should be explored by NGOs, Ministry of Health and, Support groups and other relevant agencies since they have the capacity to enhanced PMTCT of HIV in Nasarawa State, Nigeria.

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series.

This brief note aims to explain the scope in conducting large-scale serological surveys of SARS-CoV-2 to define the landscape of population immunity without overlooking the inherent uncertainty steaming from sampling design and diagnostic validity. The note completes with a succinct statistical appendix of simple methods for estimating prevalence from random population samples using imperfect diagnostic tests.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these popular distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is the upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of a random discrete variable. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches on it, we show that entropy has a universal stochastic definition which is not disorder. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept and promotes entropy as the mother of creativity and evolution. As social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether the maximum entropy, applied to the distribution of wealth quantified by annual income, can give an objective description. Using publicly available income data, we show that the income distribution is consistent with the principle of the maximum entropy. The increase of entropy is associated to increase of society’s wealth yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in development and increase of the entropy of income. Such findings are contrary to the theories of ecological economics and other theories which use the term entropy in a Malthusian perspective.

In statistics and probability theory, one of the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presents the probability density functions for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique.

As its capital, Jakarta plays a critical role in boosting Indonesia’s economic growth and setting the precedent for broader change outside of the city. One crucial avenue of inquiry to better understand, and prepare for, the future of a country so heavily impacted by disastrous weather events is understanding the effects of climate change through data. This study investigates meteorological data collected from 1996 to 2021 and compares the application of the SARIMA and the Holt-Winters methods to predict the future influence of climatic parameters on Jakarta’s weather. The performance of the SARIMA method is proven to provide better results than the Holt-Winter models and both methods showed the best performances when forecasting the humidity data. The results of the forecast are able to demonstrate the characteristic of the climate in Jakarta, with dry season ranging from May to October and wet season ranging from November to April.

The main purpose of this paper is to introduce and investigate degenerate Poisson distrib- ution which is a new extension of the Poisson distribution including the degenerate expo- nential function. We then provide several properties of the degenerate Poisson distribution such as the first and the second raw moments and di¤erence operator property. Moreover, we acquired the skewness and the kurtosis for the degenerate Poisson distribution. We also derive its moment generating function by which we define the degenerate Bell polynomials and give a connection for these polynomials related to the unsigned Stirling numbers of the …rst kind.

Admission and discharge diagnoses of in-hospital patients are often in discord. Incorrect admission diagnoses are related to increased cost of care and patient safety. Additionally, due to the seasonality of many conditions, this discord may vary across the year. In this paper, we used medical claims data to develop a methodological framework that examines these differences, for Medicare beneficiaries. We provide examples for pneumonia, a condition with seasonal implications, and aneurysm, where early detection can be life-saving. Following a Bayesian approach, our work quantifies and visualizes with time series plots the degree that any clinical condition is correctly diagnosed upon admission. We examined differences in weekly intervals, during a calendar year. The mean length of stay and hospital charges were furthermore compared between matching and non-matching {admission, discharge Dx} pairs, and 95% confidence intervals of the difference of means were estimated. We applied Statistical Process Control methods and then visualized differences, for the hospital charges and the length of stay, per week, with time series plots. Our methodology and the visualizations underline the importance of a rigorous and non-delayed diagnostic process upon admission since there are significant implications in terms of hospital outcomes and cost of care.

Expectation maximization (EM) algorithm is a powerful mathematical tool for estimating statistical parameter when data sample contains hidden part and observed part. EM is applied to learn finite mixture model in which the whole distribution of observed variable is average sum of partial distributions. Coverage ratio of every partial distribution is specified by the probability of hidden variable. An application of mixture model is soft clustering in which cluster is modeled by hidden variable whereas each data point can be assigned to more than one cluster and degree of such assignment is represented by the probability of hidden variable. However, such probability in traditional mixture model is simplified as a parameter, which can cause loss of valuable information. Therefore, in this research I propose a so-called conditional mixture model (CMM) in which the probability of hidden variable is modeled as a full probabilistic density function (PDF) that owns individual parameter. CMM aims to extend mixture model. I also propose an application of CMM which is called adaptive regressive model (ARM). Traditional regression model is effective when data sample is scattered equally. If data points are grouped into clusters, regression model tries to learn a unified regression function which goes through all data points. Obviously, such unified function is not effective to evaluate response variable based on grouped data points. The concept “adaptive” of ARM means that ARM solves the ineffectiveness problem by selecting the best cluster of data points firstly and then evaluating response variable within such best cluster. In order words, ARM reduces estimation space of regression model so as to gain high accuracy in calculation.

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

This paper explores the tuning and results of two-part models on rich datasets provided through the Casualty Actuarial Society (CAS). These data sets include BI (bodily injury), PD (property damage) and COLL (collision) coverage, each documenting policy characteristics and claims across a four year period. The datasets are explored, including summaries of all variables, then the methods for modeling are set forth. Models are tuned and the tuning results are displayed, after which we train the final models and seek to explain select predictions. All of the code will be made available on GitHub. Data was provided by a private insurance carrier to the CAS after anonymizing the data set. This data is available to actuarial researchers for well-defined research projects that have universal benefit to the insurance industry and the public. Our hope is that the methods demonstrated here can be a good foundation for future ratemaking models to be developed and tested more efficiently.

The main aim of this paper is to investigate multifarious properties and relations for the gamma distribution. The approach to reach this purpose will be introducing a special polynomial including gamma distribution. Several formulas covering addition formula, derivative property, integral representation and explicit formula are derived by means of the series manipulation method. Furthermore, two correlations including Bernoulli and Euler polynomials for gamma distribution polynomials are provided by utilizing of their generating functions.

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of the generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss generating function approach using which we derive different entropy measures. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.

Adversarial Classification (AC) is a major subfield within the increasingly important domain of adversarial machine learning (AML). Most approaches to AC so far have followed a classical game-theoretic framework. This requires unrealistic common knowledge conditions untenable in the security settings typical of the AML realm. After reviewing such approaches, we present alternative perspectives on AC based on Adversarial Risk Analysis.

We are of the opinion that during the design of a binary classifier one ought to consider adding an “I don’t know” answer. We provide the case for the introduction of this third category when a human needs to make a decision based on the answer from a binary classifier. We discuss the costs and potential benefits of its introduction. Colloquially, we have used the term “I don’t know”, but formally we refer to it as NotAvailable. A procedure to define NotAvailable predictions in binary classifiers, called all leave-one-out models (ALOOM), is presented as proof of the concept. Furthermore, we discuss the potential benefits of applying ALOOM in real life applications.

The purpose of this paper is to explore the presence of spatial and temporal effects on the calls for noise disturbance service reported to the Local Police of València (Spain) in the time period from 2014 to 2015, and investigate how some socio-demographic and environmental variables affect the noise phenomenon. The analysis is performed at the level of València's boroughs. It has been carried out using a logistic model after dichotomization of the noise incidents variable. The spatial effects consider first and second order neighbours. The temporal effects are included in the model by means of one and two weeks temporal lags. Our model confirms the presence of strong spatio-temporal effects. We also find significant associations between noise incidence and specific age groups, socio-economic status, land uses and recreational activities, among other variables. The results suggest that there is a problem of ``social'' noise in València that is not exclusively a consequence of coexistence between local residents. External factors such as the increasing number of people on the streets during weekend nights or during summer months increase severely the chances of expecting a noise incident.

A critical analysis of the classical definition of outsiders is given. Some examples show that this notion is not universal and has at least two drawbacks. Particularly, the set of outsiders may have the probability arbitrary close to one half. On the other hand, the deleting of the set of outsiders may dramatically change the value of the median.

A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as the Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we both study the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard, we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators; the multiple point Maximum A-Posteriori (MAP) estimators; an efficient class of multiple-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators; and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert-Schmidt independence criterion (HSIC) and its d-variate version (d-HSIC), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (CPT) based on the Hilbert-Schmidt conditional independence criterion (HSCIC), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socio-economic data.

The use of risk measures such as the Value at Risk (VaR) or Tail Conditional Expectation (TCE) is required by the Basel Committee on Banking Supervision in determining a bank’s risk profile. However, both measures can be shown to have shortcomings in the information that they provide to regulators and investors. In this paper we present an introduction to risk measure calculations before demonstrating the weaknesses of these measures. Through the exploration of specific cases we show how familiar yet differing risk profiles have identical values for combinations of these measures. From this evidence we recommend that a sequence of several risk measures should be used to give a more accurate representation of the risk contained on banking balance sheet.

In fisheries monitoring, catch is assumed to be a product of fishing intensity, catchability, and availability, where availability is defined as the number or biomass of fish present and catchability refers to the relationship between catch rate and the true population. Ecological monitoring programs use catch per unit of effort (CPUE) to standardize catch and monitor changes in fish populations; however, CPUE is proportional to the portion of the population that is vulnerable to the type of gear that is used in sampling, which is not necessarily the entire population. Programs often deal with this problem by assuming that catchability is constant, but if catchability is not constant, it is not possible to separate the effects of catchability and population size using monitoring data alone. This study uses individual-based simulation to separate the effects of changing environmental conditions on catchability and availability in environmental monitoring data. The simulation combines a module for sampling conditions with a module for individual fish behavior to estimate the proportion of available fish that would escape from the sample. The method is applied to the case study of the well-monitored fish species Delta Smelt (Hypomesus transpacificus) in the San Francisco Estuary, where it has been hypothesized that changing water clarity may affect catchability for long-term monitoring studies. Results of this study indicate that given constraints on Delta Smelt swimming ability, it is unlikely that the apparent declines in Delta Smelt abundance are due to an effect of changing water clarity on catchability.

Conditional heteroskedastic financial time series are commonly modelled by (G)ARCH processes. ARCH(1) and GARCH were recently established in C[0,1] and L^2[0,1]. This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of (G)ARCH processes for any order in C[0,1] and L^p[0,1]. It deduces explicit asymptotic upper bounds of estimation errors for the shift term, the complete (G)ARCH operators and the projections of ARCH operators on finite-dimensional subspaces. The operator estimaton is based on Yule-Walker equations, and estimating the GARCH operators also involves a result estimating operators in invertible linear processes being valid beyond the scope of (G)ARCH. Moreover, our results regarding (G)ARCH can be transferred to functional AR(MA).

Directed acyclic graphs (DAGs) are nonparametric causal path diagrams that have substantial utility as principled representations of disease and healthcare pathways, and of the underlying ‘data generating mechanisms’ these pathways involve. As such, DAGs provide a valuable bridge between: the aetiological knowledge, operational insight and professional experience on which clinical training and practice depend; and the more abstract epistemological and analytical considerations required to extract robust statistical insight from health and healthcare data. DAGs are nonetheless vulnerable to imperfect biomedical paradigms, partial clinical knowledge and limited empirical data. DAGs drawn under such circumstances offer limited scope for statistical insight free from cognitive, analytical or inferential bias if: they misrepresent the data generating mechanisms involved; or ignore the important role that omitted variables (whether measured, unmeasured or unacknowledged) might play therein. To address these weaknesses and broaden the appeal and application of DAGs, this chapter provides ten simple steps that educators can use to improve the analytical competence and statistical confidence of the healthcare students, qualified practitioners and experienced researchers they support. These steps use temporal logic to draw DAGs so as to: reduce reliance on uncertain knowledge, incomplete information, flawed assumptions or guesswork; and avoid, mitigate or acknowledge the errors and biases that each of these incur. The chapter comprises an accessible, non-technical overview of the perspective and thoughtfulness required to generate temporally coherent DAGs as objective representations of the probabilistic causal paths involved in context-specific data generating mechanisms. It encourages a focus on those variables operating as potential sources of analytical or inferential bias when estimating the plausible, probabilistic causal relationship between two pre-specified variables; and specifically addresses the challenges posed by: omitted; time-variant; non-asynchronous; and temporally obscure variables. The chapter includes a worked example based on a published clinical study to demonstrate how each of the steps required to generate temporally-informed DAGs can be applied to: critically appraise the analytical decisions made during applied healthcare research; and inform the decisions required when designing, undertaking and analysing primary and secondary, prospective and retrospective research. The appendices include a summary of ten recommendations for improving the reporting and interrogability of DAGs and DAG-informed analyses.

Influential Observations, which are outliers in x direction, y direction or both, remain a hitch in classical regression model fitting. Spatial regression model, with peculiar nature of outliers due to their local nature, is not free from the effect of such influential observations. Researchers have adapted some classical regression techniques to the spatial models and yielded satisfactory results. However, masking or/and swamping remain stumbling block to such methods. We obtained the spatial representation of the classical regression measures of diagnostic in general spatial model. Commonly used diagnostic measure in spatial diagnostic, the Cook's distance, is compared to some robust methods, Hi2 (using robust and non-robust measures), and classification based on generalized residuals and diagnostic generalized potentials, ISRs-Posi and ESRs-Posi, with the help of the obtained spatial prediction residuals and the spatial leverage term. Results of simulation and applications to real data have shown the advantage of the ISRs-Posi and ESRs-Posi due to classification of outliers over Cook's distance and non-robust Hsi12, which suffer from masking, and robust Hsi22 which suffer from swamping in general spatial model.

This article examines the impact of some system parameters on an industrial system composed of two dissimilar parallel units with one repairman. The active unit may fail due to essential factors like aging or deteriorating, or exterior phenomena such as Poisson shocks that occur at various time periods. Whenever the value of a shock is larger than the specified threshold of the active unit, the active unit will fail. The article assumes that the repairman has the right to take any of two decisions at the beginning of the system operation: either a takes a vacation if the two units work in a normal way, or stay in the system to monitor the system until the first system failure. In case of having a failure in any of the two units during the absence of the repairman, the failing unit will have to wait until the repairman is called back to work. We suppose that the value of every shock is assumed to be i.i.d. with some known distribution. The length of the repairman’s vacation, repair time, and recall time are arbitrary distributions. Various reliability measures have been calculated by the supplementary variable technique and the Markov’s vector process theory. At last, numerical computation and graphical analysis have been given for a particular case to validate the derived indices.

The purpose of this study was to identify the factors that affect the mortality among adult HIV/TB co-infected patients and to see the nutritional difference among mortality in residence level. Retrospective cohort studies of 417 patients which fulfill our criteria were included. Multilevel logistic regression models were used. MLwiN and SPSS software are used to estimate the parameter. The variance of the random factor in the empty model was significant which indicates that there were residential differences in TB-HIV co-infected mortality and it shows multilevel analysis was an appropriate approach for further analysis. The prevalence of HIV/TB co-infected patients' death was 12.9% in study time. Functional status, age of patients, WHO clinical stages, nutritional status, CD4 counts, regimen, and BMI were found to be significant determinants of HIV/TB co-infected mortality. In our study, patients with the bedridden category of functional status, the fourth stages of WHO clinical stages (stage IV), patients with higher age, patients whose treatments were second-line regimen and low CD4 cell counts were more at risk of death. The study also revealed that; poor nutritional status increased the risk of mortality among HIV/TB co-infected patients and it varies among the residence of the patients (rural area were more at risk).

The aim of this work is to study generalizations of the notion of mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the Weak Law of Large Numbers in the same way that the ordinary mean relates to the Strong Law. We propose a further generalization, also based on an improper integral, called the doubly weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions, We also consider generalizations arising from Abel-Feynman type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g. probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g. precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known bi-normal fitting model, we discuss a new approach which embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.

(1) Background: In nervous system information is conveyed by a sequence of action potentials, called spikes-trains. As MacKay and McCulloch proposed, spike-trains can be represented as bits sequences coming from Information Sources. Previously, we studied relations between Information Transmission Rates (ITR) carried out by the spikes, their correlations, and frequencies. Here, we concentrate on the problem of how spikes fluctuations affect ITR. (2) Methods: The Information Theory Method developed by Shannon is applied. Information Sources are modeled as stationary stochastic processes. We assume such sources as two states Markov processes. As a spike-trains' fluctuation measure, we consider the Standard Deviation sigma, which, in fact, measures average fluctuation of spikes around the average spike frequency. (3) Results: We found that character of ITR and signal fluctuations relation strongly depends on the parameter s which is a sum of transitions probabilities from no spike state to spike state and vice versa. It turned out that for smaller s (s<1) the quotient ITR\sigma has a maximum and can tend to zero depending on transition probabilities. While for s large enough (1<s) the ITR\sigma is separated from 0 for each s. Similar behavior was observed also when we replaced Shannon entropy terms in Markov entropy formula by their approximation with polynomials. We also show that the ITR quotient by Variance behaves in a completely different way. (4) Conclusions: Our results show that for large transition parameter s the Information Transmission Rate by sigma will never decrease to zero. Specifically, for 1<s<1.7 the ITR will be always, independently on transition probabilities which form this s, above the level of fluctuations, i.e. in this case we have sigma<ITR. Thus, we conclude that in a more noisy environment, to get appropriate reliability and efficiency of transmission, Information Sources with higher tendency of transition from the state no spike to spike state and vice versa should be applied.

We propose a new estimator for creating expansion factors for survey plots in the USDA Forest Inventory and Analysis program. This is a regularized version of the raking estimator widely used in sample surveys. The regularized raking method differs from other predictive modeling methods for integrating survey and ancillary data in that it produces a single set of expansion factors that can have general purpose use to produce small area estimates and wall-to-wall maps of any plot characteristic. This method also differs from other more widely used survey techniques, such of GREG estimation, in that it is guaranteed to produce positive expansion factors. We extend the previous method here to include cross-validation, and provide a comparison to expansion factors between the regularized raking and ridge GREG survey calibration.

A single Information security is of pivotal concern for consistently streaming information over the widespread internetwork. The bottleneck flow of incoming and outgoing data traffic introduces the issue of malicious activities taken place by intruders, hackers and attackers in the form of authenticity desecration, gridlocking data traffic, vandalizing data and crashing the established network. The issue of emerging suspicious activities is managed by the domain of Intrusion Detection Systems (IDS). The IDS consistently monitors the network for identifica-tion of suspicious activities and generates alarm and indication in presence of malicious threats and worms. The performance of IDS is improved by using different signature based machine learning algorithms. In this paper, the performance of IDS model is determined using hybridization of nestrov-accelerated adaptive moment estimation –stochastic gradient descent (HNADAM-SDG) algorithm. The performance of the algorithm is compared with other classi-fication algorithms as logistic regression, ridge classifier and ensemble algorithm by adapting feature selection and optimization techniques

The parameters of logistic regression models are usually obtained by the method of maximum likelihood (ML). However, in analyses of small data sets or data sets with unbalanced outcomes or exposures, ML parameter estimates may not exist. This situation has been termed “separation” as the two outcome groups are separated by the values of a covariate or a linear combination of covariates. To overcome the problem of non-existing ML parameter estimates, applying Firth’s correction (FC) was proposed. In practice, however, a principal investigator might be advised to “bring more data” in order to solve a separation issue. We illustrate the problem by means of an examples from colorectal cancer screening and ornithology. It is unclear if such an increasing sample size (ISS) strategy that keeps sampling new observations until separation is removed improves estimation compared to applying FC to the original data set. We performed an extensive simulation study where the main focus was to estimate the cost-adjusted relative efficiency of ML combined with ISS compared to FC. FC yielded reasonably small root mean squared errors and proved to be the more efficient estimator. Given our findings, we propose not to adapt the sample size when separation is encountered but to use FC as the default method of analysis whenever the number of observations or outcome events is critically low.

We present a formalism to assess the safety of the COVID19 vaccines and infer a causal relation between vaccine administration and adverse effects, in particular death. We use data on adverse effects from VAERS covering the time interval [01-10-2020, 31-12-2021] (downloaded on 1 Feb 2022). We measure a vaccine fatality rate of order 0.01 for all vaccine manufacturers and identify a strong heterogeneity in the vaccine toxicity across vaccine lots, spanning up to four orders of magnitude. We compute the correlation between vaccination dates and death dates, and produce an estimate of the time lag that maximises the correlation, finding that the onset of adverse effects happened statistically (i.e. 32-41 percentiles) within one day after the vaccine administration and that death happened statistically (i.e. 22-50 percentiles) within about two weeks after the vaccine administration. These results provide data-based insights that can guide public health measures and health insurance policies.

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of the aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided.

This study aims to apply a Recommendation System with Content Based Filtering method with Jaccard Similarity and Cosine Similarity algorithms on the E-Learning Platform. Recommendation systems deal with how to provide personalized recommendations to users efficiently. The Content Based Filtering method with Jaccard Similarity and Cosine Similarity algorithms can be used to calculate the similarity value between E-Courses on the E-Learning Platform. Implementation for Recommendation System using Google Colaboratory with Python programming language. In the application of the Recommendation System dataset, Coursera Free Dataset consists of 975 instances. The recommendation results use the Jaccard Similarity algorithm with an average similarity value of 0.3 while the value of Cosine Similarity with the average similarity value is 0.6 where the similarity value of Cosine Similarity is higher. Based on the results of the Mean Absolute Error in the low recommendation system, the average MAE value for all iterations of Jaccard Similarity algorithm is 0.013 and for the Cosine Similarity algorithm the average MAE value for all iterations is 0.014. This shows that the Recommendation System with Jaccard Similarity and Cosine Similarity algorithms can be used on the E-Learning Platform to provide efficiency solutions for personalized recommendations.

Link prediction is an unbalanced early retrieval problem, whose goal is to prioritize a small cohort of positive links on top of a list largely populated by unlabelled links. Differently from binary classification, here the evaluation focuses on how the predictor prioritizes the positive class because, in practice, a negative class does not exist. Previous studies explained that AUC-ROC is not apt for unbalanced class problems and is misleading for early retrieval problems, therefore standard AUC-ROC is not appropriate for evaluation of link prediction. However, some scholars argue that an AUC-ROC like evaluation accounting for the relative positioning of the few positive links among the vastness of unlabelled links remains a valid concept to pursue. Here we propose the area under the magnified ROC (AUC-mROC), a new measure that adjusts the standard AUC-ROC to work also for unbalanced early retrieval problems such as link prediction.

We investigate the power of time series analysis based on a variety of information-theoretic approaches from statistics (AIC, BIC) and machine learning (Minimum Message Length) - and we then compare their efficacy with traditional time series model and with hybrids involving deep learning. More specifically, we develop AIC, BIC and Minimum Message Length (MML) ARMA (autoregressive moving average) time series models - with this Bayesian information-theoretic MML ARMA modelling already being new work. We then study deep learning based algorithms in time series forecasting, using Long Short Term Memory (LSTM), and we then combine this with the ARMA modelling to produce a hybrid ARMA-LSTM prediction. Part of the purpose of the use of LSTM is to seek capture any hidden information in the residuals left from the traditional ARMA model. We show that MML not only outperforms earlier statistical approaches to ARMA modelling, but we further show that the hybrid MML ARMA-LSTM models outperform both ARMA models and LSTM models.

Evidence-based medicine (EBM) is in crisis, in part due to bad methods, which are understood as misuse of statistics that is considered correct in itself. This article exposes two related common misconceptions in statistics, the effect size (ES) based on correlation (CBES) and a misconception of contingency tables (MCT). CBES is a fallacy based on misunderstanding of correlation and ES and confusion with 2 × 2 tables, which makes no distinction between gross crosstabs (GCTs) and contingency tables (CTs). This leads to misapplication of Pearson’s Phi, designed for CTs, to GCTs and confusion of the resulting gross Pearson Phi, or mean-square effect half-size, with the implied Pearson mean square contingency coefficient. Generalizing this binary fallacy to continuous data and the correlation in general (Pearson’s r) resulted in flawed equations directly expressing ES in terms of the correlation coefficient, which is impossible without including covariance, so these equations and the whole CBES concept are fundamentally wrong. MCT is a series of related misconceptions due to confusion with 2 × 2 tables and misapplication of related statistics. The misconceptions are threatening because most of the findings from contingency tables, including CBES-based meta-analyses, can be misleading. Problems arising from these fallacies are discussed and the necessary changes to the corpus of statistics are proposed resolving the problem of correlation and ES in paired binary data. Since exposing these fallacies casts doubt on the reliability of the statistical foundations of EBM in general, we urgently need to revise them.

Guessing effects frequently occur in testing data in educational or psychological applications. Different item response models have been proposed to handle guessing effects in dichotomous test items. However, it has been pointed out in the literature that the oftenemployed three-parameter logistic model poses implausible assumptions regarding the guessing process. The four-parameter guessing model has been proposed as an alternative to circumvent these conceptual issues. In this article, the four-parameter guessing model is compared with alternative item response models for handling guessing effects through a simulation study and an empirical example. It turned out that model selection for item response models should be rather based on the AIC than the BIC. However, the RMSD item fit statistic used with typical cutoff values was found to be ineffective in detecting misspecified item response models. Furthermore, sufficiently large sample sizes are required for sufficiently precise item parameter estimation. Moreover, it is argued that the criterion of statistical model fit should not be the sole criterion of model choice. The item response model used in operational practice should be valid with respect to the meaning of the ability variable and the underlying model assumptions. In this sense, the four-parameter guessing model could be the model of choice in educational large-scale assessment studies.

To detect aberrant human behaviors from large volume of passive data collected by smartphones in real time, we propose an online anomaly detection method using Hotelling’s T-squared test. The test statistic is a weighted average, with more weight on the between-individual component when there are little data available for the individual and more weight on the within-individual component when the data are adequate. The algorithm takes only O(1) run time in each update and the required memory usage is fixed after a pre-specified number of updates. The performance of the proposed method, in terms of accuracy, sensitivity and specificity, is consistently better than or equal to the offline method that it builds upon depending on the sample size of the individual data.

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

Background: We considered a problem of inference in epidemiology when cumulative exposure is the true dose metric for disease, but investigators are only able to measure its duration on each subject. Methods: We undertook theoretical analysis of the problem in the context of a continuous response caused by cumulative exposure, when duration and intensity of exposure follow log-normal distributions, such that analysis by linear regression is natural. We present a Bayesian method to adjust duration-only analysis to incorporate partial knowledge about the relationship between duration and intensity of exposure and illustrate this method in the context of association of smoking and lung function. Results: We derive equations that (a) describe under what circumstances bias arises when duration of exposure is used as a proxy of cumulative exposure, (b) quantify the degree of such bias and loss of precision, and (c) describe how knowledge about relationship of duration and intensity of exposure can be used to recover an estimate of the effect of cumulative exposure when only duration was observed on every subject. Conclusions: Under our assumptions, when duration and intensity of exposure are either independent or positively correlated, we can be more confident in qualitatively interpreting the direction of effects that arise from use of duration of exposure per se. To make reliable inference about the magnitude of effect of cumulative exposure on the outcome, we can use external information on the relationship between duration and intensity of exposure even if intensity of exposure is not available at the individual level.

We propose a new ensemble classification algorithm, named Super Random Subspace Ensemble (Super RaSE), to tackle the sparse classification problem. The proposed algorithm is motivated by the Random Subspace Ensemble algorithm (RaSE). The RaSE method was shown to be a flexible framework that can be coupled with any existing base classification. However, the success of RaSE largely depends on the proper choice of the base classifier, which is unfortunately unknown to us. In this work, we show that Super RaSE avoids the need to choose a base classifier by randomly sampling a collection of classifiers together with the subspace. As a result, Super RaSE is more flexible and robust than RaSE. In addition to the vanilla Super RaSE, we also develop the iterative Super RaSE, which adaptively changes the base classifier distribution as well as the subspace distribution. We show the Super RaSE algorithm and its iterative version perform competitively for a wide range of simulated datasets and two real data examples. The new Super RaSE algorithm and its iterative version are implemented in a new version of the R package RaSEn.

Stage of cancer is a discrete ordinal response that indicates aggressiveness of disease and is often used by physicians to determine the type and intensity of treatment to be administered. For example, the FIGO stage in cervical cancer is based on the size and depth of the tumor as well as the level of spread. It may be of clinical relevance to identify molecular features from high-throughput genomic assays that are associated with stage of cervical cancer, to elucidate pathways related to tumor aggressiveness, identify improved molecular features that may be useful for staging, and identify therapeutic targets. High-throughput RNA-Seq data and corresponding clinical data (including stage) for cervical cancer patients has been made available through The Cancer Genome Atlas Project (TCGA). We recently described penalized Bayesian ordinal response models that can be used for variable selection for over-parameterized datasets such as the TCGA-CESC dataset. Herein, we describe our ordinalbayes R package, available from the Comprehensive R Archive Network (CRAN), which is capable of fitting cumulative logit models when the outcome is ordinal and the number of predictors exceeds the sample size, P>N, such as for TCGA data. We demonstrate use of this package through application to TCGA cervical cancer dataset. Our ordinalbayes package can be used to fit models to high-dimensional dataset and effectively performs variable selection.

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders.

Statistical modeling of lifetime data plays an essential role in a wide range of practical fields, such as health and engineering. There have been a lot of studies done to develop statistical models that can better describe health data than traditional models. For the first time, we pioneer a novel family of continuous probability distributions called the generalized odd beta prime generalized (GOBP-G) family of distributions. The cumulative distribution and probability density functions of the new family are presented. A new generalization of the Weibull distribution called "generalized odd beta prime-Weibull" (GOBPW) is proposed using the pioneered GOBP-G family. The mixture representations of the new distribution are defined and derived. Some formal statistical properties of the GOBPW distribution, such as the moments, moment generating function, incomplete moments, information generating function, entropies, stress-strength function, quantile function, and order statistics, are derived. The estimation of the parameters of the proposed distribution is evaluated using the maximum likelihood estimation approach. Different cancer disease data sets, such as the bladder, head and neck, acute bone, and blood cancers, are used to illustrate the applicability and usefulness of the new model and were compared using several statistical accuracy measures with that of well-established extended Weibull distributions, which are the beta modified Weibull distribution, Kumaraswamy modified Weibull distribution, gamma generalized modified Weibull distribution, gamma log-logistic Weibull distribution, and beta log-logistic Weibull distribution. The results show that the proposed model gives better results than the competitive models. This study could guide the relevant stakeholders in choosing a suitable statistical model for the health data instead of relying on traditional models to enhance decision-making.

Objectives: This paper presents a statistical review of modelling simulations for frequency and sensitivity of COVID-19 testing paradigms. Methods: We performed a review of preprints and published articles on PubMed from January 1, 2020 – March 1, 2021 using the search terms “COVID screening testing”, “COVID testing frequency”, “COVID testing frequency screening” and “SARS-CoV-2 testing frequency”.Results: Several authors’ conclusions support the claim that test frequency and test sensitivity both play a role in reducing SARS-CoV-2 transmission. We highlight the interplay between frequency of testing, test sensitivity and the speed at which test results are available in our review. Conclusions: Evidence suggests that sensitivity and frequency of testing both play a part in decreasing transmission of disease. We conclude that, overall, test sensitivity plays less of a role in reducing disease transmission in a population compared to the frequency of testing and how quickly test results are available.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

Classification predictive modeling involves the accurate assignment of observations in a dataset to target classes or categories. There is an increasing growth of real-world classification problems with severely imbalanced class distributions. In this case, minority classes have much fewer observations to learn from than those from majority classes. Despite this sparsity, a minority class is often considered the more interesting class yet developing a scientific learning algorithm suitable for the observations presents countless challenges. In this article, we suggest a novel multi-class classification algorithm specialized to handle severely imbalanced classes based on the method we refer to as SAMME.C2. It blends the flexible mechanics of the boosting techniques from SAMME algorithm, a multi-class classifier, and Ada.C2 algorithm, a cost-sensitive binary classifier designed to address highly class imbalances. Not only do we provide the resulting algorithm but we also establish scientific and statistical formulation of our proposed SAMME.C2 algorithm. Through numerical experiments examining various degrees of classifier difficulty, we demonstrate consistent superior performance of our proposed model.

The opioid crisis in the United States has had devastating effects on communities across the country, leading many states to pass legislation that limits the prescription of opioid medications in an effort to reduce the number of overdose deaths. This study evaluates the impact of two categories of PDMP and Pill Mill regulations on the supply of opioid prescriptions at the level of dispensers and distributors (excluding manufacturers) using ARCOS data. The study uses a difference-in-difference method with a two-way fixed design to analyze the data. The study finds that both of the regulations are associated with reductions in the volume of opioid distribution. However, the study reveals that these regulations may have unintended consequences, such as shifting the distribution of controlled substances to neighboring states. For example, in Tennessee, the implementation of Operational PDMP regulations reduces in-state distribution of opioid drugs by 3.36% (95% CI, 2.37 to 4.3), while the out-of-state distribution to Georgia, which did not have effective PDMP regulations in place, increases by 16.93% (95% CI, 16.42 to 17.44). Our studies emphasize that policymakers should consider the potential for unintended distribution shifts of opioid drugs to neighboring states with laxer regulations as well as varying impacts on different dispenser types.

We address the process of discounting in random environments which allows to value the far future in economic terms. We review several approaches to the problem regarding different well-established stochastic market dynamics in the continuous-time context and include the Feynman-Kac approach. We also review the relation between bond pricing theory and discount and introduce the market price of risk and the risk neutral measures from an intuitive point of view devoid of excessive formalism. We provide the discount for each economic model and discuss their key results. We finally present a summary of our previous empirical studies on several countries of the long-run discount problem.

The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration experiments.

In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh Weibull (RW) distribution based on progres-sive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley and Tierney-Kadane's approximation method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes esti-mates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Real lifetime data sets belonging to the cancer types as bladder cancer, head and neck cancer, and leukemia are used to illustrate the emprical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals.

In many practical applications, it is more convenient to characterize the quality of production processes or service operations throughout the count of nonconformities. In the context of SPC, nonconformities are usually assumed to appear according to the binomial probability model. The conventional way for monitoring nonconformities involves Shewhart-type control procedures based on both constant and time-varying sample sizes. In this article, an EWMA scheme is proposed for monitoring the fraction of nonconforming items with time-varying sample sizes. The proposed control chart is referred to as the EWMAG-B and can be easily adapted to work with a constant sample size by fixing it at a needed value. By means of simulation, it was found out that the EWMAG-B chart outperforms the conventional p control chart in Phase II while detecting changes in the process level is wanted.

In this note, I analyze the data generated by M. Fodje's (2013) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions shows that they make use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signaling. Fodje's coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.

In many Bayesian computations, first, we obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining their marginals for each variable and computing the expectations are difficult and costly. This problem becomes even more difficult in high dimensional quandaries, which is an important issue in inverse problems. We may then try to propose a surrogate expression with which we can do approximate computations. Often a separable expression approximation can be useful enough. The Variational Bayesian Approximation (VBA) is a technique that approximates the joint distribution $p$ with an easier, for example separable, one $q$ by minimizing Kullback–Leibler Divergence $KL(q|p)$. When $q$ is separable in all the variables, the approximation is also called Mean Field Approximation (MFA) and so $q$ is the product of the approximated marginals. A first standard and general algorithm is alternate optimization of $KL(q|p)$ with respect to $q_i$. A second general approach is its optimization in the Riemannian manifold. However, in this paper, for practical reasons, we consider the case where $p$ is in the exponential family and so is $q$. For this case, $KL(q|p)$ becomes a function of the parameters $\thetab$ of the exponential family. Then, we can use any other optimization algorithm to obtain those parameters. In this paper, we compare three optimization algorithms: standard alternate optimization, a gradient-based algorithm and a natural gradient algorithm and study their relative performances on three examples.

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds, it is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.

Measurement uncertainty is typically expressed in terms of a symmetric interval , where denotes the measurement result and the expanded uncertainty. However, in the case of heteroscedasticity, symmetric uncertainty intervals can be misleading. In this paper, a different approach for the calculation of uncertainty intervals is introduced. This approach is applicable when a validation study has been conducted with samples with known concentrations. It will be shown how, under certain circumstances, asymmetric uncertainty intervals arise quite naturally and lead to more reliable uncertainty intervals.

Let $f(t)$ be a characteristic function. The question on infinite divisibility of $g_{2k}(t)=f^{(2k)}(t)/f^{(2k)}(0)$ is considered. There are given the condition for that function not to be infinite divisible. Some examples of infinite divisibility of $g_{2k}(t)$ are given.

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly without any transformation (e.g. normalization). We illustrate the method in a number of synthetic and real-world applications with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded form below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

A method for noise reduction of spectra based on the adaptive application of the Savitsky-Golay polynomial filter is presented. A polynomial approximation is calculated at all points of the spectrum and for all window sizes. The weighted sum of all polynomials containing the point to be processed is used as the result. The weighting factors are calculated by evaluating the quality of the fit. This paper proposes two evaluation functions. The performance of the presented method is compared with the Savitsky-Golay method and the wavelet noise reduction method. The proposed approach provides good noise reduction performance without using user-entered parameters.

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980s. On the other hand, deep learning methods have boosted the capacity of machine learning algorithms and are now being used for non-trivial applications in various applied domains. But training a fully-connected deep feed-forward network by gradient-descent backpropagation is slow and requires arbitrary choices regarding the number of hidden units and layers. In this paper, we propose near-optimal neural regression trees, intending to make it much faster than deep feed-forward networks and for which it is not essential to specify the number of hidden units in the hidden layers of the neural network in advance. The key idea is to construct a decision tree and then simulate the decision tree with a neural network. This work aims to build a mathematical formulation of neural trees and gain the complementary benefits of both sparse optimal decision trees and neural trees. We propose near-optimal sparse neural trees (NSNT) that is shown to be asymptotically consistent and robust in nature. Additionally, the proposed NSNT model obtain a fast rate of convergence which is near-optimal up to some logarithmic factor. We comprehensively benchmark the proposed method on a sample of 80 datasets (40 classification datasets and 40 regression datasets) from the UCI machine learning repository. We establish that the proposed method is likely to outperform the current state-of-the-art methods (random forest, XGBoost, optimal classification tree, and near-optimal nonlinear trees) for the majority of the datasets.

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

In this note, we provide some effective treatments of a general linear model with adding-up restrictions via algebraic operations of given vectors and matrices in the model, including analytic expressions of the well-known ordinary least-squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the unknown parameters in the model.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

A multi-server parallel system dispatches the incoming job, which contains kn tasks into n servers. A job is considered to be computed if all the tasks associated with the job are processed. One job’s tasks can be encoded into at least kn “replicas” such that the job is considered to be served if any kn replicas finishing computation. In this paper, we analyze the random scheduling policy of a multi-server computing system under discrete time model in terms of Quality of Exponent (QoE), which is defined as the probability exponent that a typical job can be computed within a given number of time slots. We let kn/n be a constant. Assuming that any task of any job can be randomly dispatched by a “scheduler” to any server, and computing each task takes exactly one time slot. We divide the calculation of probability exponent into two parts, exponent of numerator and exponent of denominator. For the denominator, we give the almost exact exponent using Lagrange multiplier method, while for the numerator, an upper bound of the numerator’s exponent is provided. In addition, we also express the exponent in terms of information theoretical quantities and reconsider both of exponents in the context of large deviation theory.

For more than half a century, Manfred Deistler has been contributing to the construction of the rigorous theoretical foundations of the statistical analysis of time series and more general stochastic processes. Half a century of unremitting activity is not easily summarized in a few pages. In this short note, we chose to concentrate on a relatively little-known aspect of Manfred's contribution which nevertheless had quite an impact on the development of one of the most powerful tools of contemporary time series and econometrics: dynamic factor models.

Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modelling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. Mathematical and statistical properties of the novel distribution are examined, including quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method was carried out, and applications to environmental and engineering data were also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered.

Noisy data is always encountered in real applications, such as bioinformatics, neuroimage and remote sensing. Existing methods mainly consider linear or generalized linear errors-in-variables regression, while relatively little attention is paid for the multivariate response case, and how to evaluate the estimation performance under perturbed covariates is still an open question. In this paper, we consider the information-theoretic limitations of estimating a low-rank matrix in the multi-response errors-in-variables regression model. By application of the information theory and statistical techniques on concentration inequalities, the minimax lower bound is provided in terms of the squared Frobenius loss, which recaptures the rate provided under the clean covariate assumption in previous literatures. Hence our result further indicates that though under the more realistic errors-in-variables situation, no more samples are required so as to achieve a rate-optimal estimation.

Notion of median in one dimension is a foundational element in nonparametric statistics. It has been extended to multi-dimensional cases both in location and in regression via notions of data depth. Regression depth (RD) and projection regression depth (PRD) represent the two most promising notions in regression. Carrizosa depth DC is another depth notion in regression. Depth induced regression medians (maximum depth estimators) serve as robust alternatives to the classical least squares estimator. The uniqueness of regression medians is indispensable in the discussion of their properties and the asymptotics (consistency and limiting distribution) of sample regression medians. Are the regression medians induced from RD, PRD, and DC unique? Answering this question is the main goal of this article. It is found that only the regression median induced from PRD possesses the desired uniqueness property. The conventional remedy measure for non-uniqueness, taking average of all medians, might yield an estimator that no longer possesses the maximum depth in both RD and DC cases. These and other findings indicate that the PRD and its induced median are highly favorable among their leading competitors.

A random variable X that is base b Benford will not in general be base c Benford when c is not equal to b. This paper builds on two of my earlier papers and is an attempt to cast some light on the issue of base dependence. Following some introductory material, the “Benford spectrum” of a positive random variable is introduced and known analytic results about Benford spectra are summarized. Some standard machinery for a “Benford analysis” is introduced and combined with my method of “seed functions” to yield tools to analyze the base c Benford properties of a base b Benford random variable. Examples are generated by applying these general methods to several families of Benford random variables. Berger and Hill's concept of “base-invariant significant digits” is discussed. Some potential extensions are sketched.

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph’s degree.

Regression models are mostly used in all fields of sciences for modelling the relationship between a dependent variable and independent variable(s). The least square method is often used to estimate the parameters in a linear model because it is the best linear unbiased estimator. These estimates can only be reliable if the assumption of normality is satisfied. In some cases the dependent variable might be bimodal and shows a non-linear relationship with the independent variable(s). In this case, a non-linear model should be used. In non-linear model, the standard errors are often obtained by linearizing the nonlinear function around the parameter, assuming central limit theorem. After the linearization, the least square parameter estimates are obtained. It should be noted that the error of the non-linear model is different from that of the transformed linear model. Thus, there is a need to transform back to the original non-linear model. In this note, a novel non-linear function was developed into a non-linear regression model, called Normal-Power model. The least square method was used to estimate the parameter of the transformed model. Its usefulness in regression model was demonstrated using real data of Nigeria Economy-Tourism model.

Using Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) in their information version, this paper extends their theoretical framework to incorporate instantaneous Granger Causality (iGC)’s frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger Connectivity where interactions mediated without delay between time series can be easily detected.

Three-dimensional reconstruction plays an important role in assisting doctors and surgeons in diagnosing bone defects’ healing progress. Common three-dimensional reconstruction methods include surface and volume rendering. As the focus is on the shape of the bone, volume rendering is omitted. Many improvements have been made on surface rendering methods like Marching Cubes and Marching Tetrahedra, but not many on working towards real-time or near real-time surface rendering for large medical images, and studying the effects of different parameter settings for the improvements. Hence, in this study, an attempt towards near real-time surface rendering for large medical images is made. Different parameter values are experimented on to study their effect on reconstruction accuracy, reconstruction and rendering time, and the number of vertices and faces. The proposed improvement involving three-dimensional data smoothing with convolution kernel Gaussian size 0.5 and mesh simplification reduction factor of 0.1, is the best parameter value combination for achieving a good balance between high reconstruction accuracy, low total execution time, and a low number of vertices and faces. It has successfully increased the reconstruction accuracy by 0.0235%, decreased the total execution time by 69.81%, and decreased the number of vertices and faces by 86.57% and 86.61% respectively.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.

Water resource management and flood forecasting are crucial societal and financial stakes requiring reliable predictions of flow parameters (depth, velocity), the accuracy of which is often limited by uncertainties in hydrodynamic numerical models. In this study, we assess the effect of two uncertainty sources, namely breach characteristics induced by overtopping and the roughness coefficient, on water elevations and inundation extent. A two-dimensional (2D) hydraulic solver was applied in a Monte Carlo integration framework to a reach of the Loire river (France) including about 300 physical parameters. Inundation hazard maps for different flood scenarios allowed highlighting the impact of the breach development chronology. A special attention was paid to proposing a relevant sensitivity analysis to exam the factors influencing the depth and extent of flooding. The spatial analysis of vulnerability area induced by a levee breach width exhibits that, with increasing the flood discharge, the rise of the parameter influence is accompanied by a more localized spatial effect. This argues for a local analysis to allow a clear understanding of the flood hazard. The physical interpretation, highlighted by a global sensitivity analysis, showed precisely the dependence of the flood simulation on the main factors studied, i.e. the roughness coefficients and the characteristics of the breaches.

Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam's razor, machine learning, and password guessing.

Multilevel functional principal components analysis (mFPCA) is used to treat dynamical changes in shape in this article. Results of standard (single-level) FPCA are presented here also as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single “outcome” variable) that contains two distinct classes of trajectory with time. MC simulation is also used to create multivariate data of sixteen 2D points that represent (broadly) an eye; this data also has two distinct classes of trajectory (an eye blinking and an eye widening in surprise). This is followed-up by an application of mFPCA and single-level FPCA to “real” data consisting of twelve 3D landmark outlining the mouth that are tracked over all phases of a smile. By consideration of eigenvalues, results for the MC datasets find correctly that variation due to differences in groups between the two classes of trajectories variation are larger than variation within each group. In both cases, differences in standardized component scores between the two groups are observed, as expected. Modes of variation are shown to model the univariate MC data correctly, and good model fits are found for both the “blinking” and “surprised” trajectories for the MC “eye” data. Results for the “smile” data show that the smile trajectory is modelled correctly, namely: the corners of the mouth are drawn backwards and wider during a smile. Furthermore, the first mode of variation at level 1 of the mFPCA model show only subtle and minor changes in mouth shape due to sex, whereas the first mode of variation at level 2 of the mFPCA model govern whether the mouth is upturned or downturned. These results are all an excellent test of mFPCA, which show that mFPCA presents a viable method of modelling dynamical changes in shape.

This article presents the results of the consideration of the Bertrand paradox in terms of geometric probability theory. Although the method and conclusions of this article are straightforward, no equivalent studies were found when reviewing the relevant literature. This could be conditioned by the fact that the hypotheses presented in this research have low intuitive obviousness and, in contrast, could be due to the historically established agreement regarding the issue. This article shows that out of three classical solutions to the problem described by Bertrand, two methods are inconsistent with the claimed relative objectivity. Although the remaining solution (1/4) seems to be the most correct, we cannot claim that we have exhaustively ruled out all aspects that could reduce its adequacy to solve the problem.

Quantile regression model is widely used in variable relationship research of general size data, due to strong robustness and more comprehensive description of the response variables' characteristics. With the increase of data size and data dimension, there have been some studies on high-dimensional quantile regression under the classical statistical framework, including higher-efficient frequency perspective, which is however at cost of randomness quantification, or lower-efficient Bayesian method based on MCMC sampling. To overcome these problems, we propose the high-dimensional quantile regression with Spike-and-Slab Lasso penalty based on variational Bayesian (VBSSLQR), which can not only improve the computational efficiency but also measure the randomness via variational distributions. The simulation studies and real data analysis illustrate that the proposed VBSSLQR method is superior to or equivalent to other quantile and non-quantile regression methods (including Bayesian and non-Bayesian methods), and its efficiency is higher than any other method.

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained increasing attention due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring for future research.

The article proposes a method for determining the p-value of correlations in compositional data, i.e., those data that arise as a result of dividing the original values by their sum. Data organized in this way are typical for many fields of knowledge, but there is still no consensus on methods for interpreting correlations in such data. In a space closed by normalizing quantity, correlation coefficients behave differently than under normal conditions: their probabilities of occurrence do not coincide with those inherent in the standard scale of estimates. In the tens of the new millennium, almost all newly emerging methods for estimating correlation in compositional data began to require mandatory log-transformation of the variable values. In the method proposed here there are no log-transformations. We return to the early stages of attempting to solve the problem and rely on negative shifts in correlations in the multinomial distribution. In modeling the data, we use a hybrid method that combines the hypergeometric distribution with the distribution of any other law. During our work on the calculation method, we found that the number of degrees of freedom in compositional data measures discretely only when all the normalizing sums are equal and that it decreases when the sums are not equal, becoming a continuously varying quantity. Estimation of the number of degrees of freedom and the strength of its influence on the magnitude of the shift in the distribution of correlation coefficients is the basis of the proposed method.

Two extensions of the generalized double Lomax distribution are introduced - the spliced-scale generalized double Lomax distribution and the exponentiated generalized double Lomax distribution. Their properties are studied. Usefulness of the new distributions is shown by fitting them to stock returns datasets.

Sword-duels are interesting, from a game-theoretical perspective, as they correspond to sudden-death interactions between players (i.e., defeat means removal from the game), and where victory/defeat depend on not just skill, but also luck. Analyzing probabilities of victory streaks, given a certain level of self and others' skill, is thus relevant for any application domain that can be modeled in the same way. This paper takes inspiration from Miyamoto Musashi, famously undefeated for 61 duels, and implements a Markov-chain Monte-Carlo simulation approach to evaluate this scenario. Results suggest that a 61 victory streak can be probabilistically observed when skill level is roughly 6.5 times that of the average duelist, and with 95\% confidence when skill level is roughly 1000 times that of the average duelist. More generally, this paper provides a method for determining chances of victory streaks in game-theoretical sudden-death encounters, when both "skill" and "luck" contribute to the outcome of the encounter. Specific scenarios can be modeled by modifying the utilized Markov chain and adjusting sampled distributions as required.

In recent times, there has been a growing interest in the use of control charts as a feedback process monitoring technique. Particularly, CUSUM schemes have been proven to be efficient for monitoring processes where the magnitude of the sustained mean shifts is small or moderate. However, because of the constant control limits, the detection ability of CUSUM schemes becomes slow at the initial set-up of the process. The fast initial response FIR feature has often been used to enhance it at the process startup. Meanwhile, the dynamism of real-life problems has always encouraged a more sensitive CUSUM scheme capable of detecting process shifts more rapidly. In this paper, an improved CUSUM scheme for monitoring process mean is proposed. This scheme will be substantial for monitoring processes whose observations are obtained at a distant time interval for example hourly, daily or weekly and where the sustained shifts are assumed to be small or moderate. To demonstrate the practical applications of the proposed scheme, we present its real-life application using datasets from a bottling company and petroleum refinery laboratory.

In the era of big data with increasingly complex data structures and ever-larger data scales, matrix-type data are becoming highly valued and their applications in the fields of medicine, industry, education, geography, and astronomy are growing in extent. In recent years, significant progress has been made in the practical use of matrix variable t-distribution finite mixture models for handling data in order to address the issues of multi-subgroup structures and long data tails. In this paper, the expectation-maximization (EM) algorithm with penalized maximum likelihood is proposed to resolve the problem of the unbounded nature of the likelihood function applied to the model by considering the degeneracy of the variance-covariance matrix of this model. Our data were analyzed through simulations and real data, and the results demonstrate that our model is effective in both preventing the likelihood function from being unbounded and in ensuring the accuracy of the estimated parameters of the EM algorithm.

This paper focuses on the so-called proportional intensity-based software reliability models (PI-SRMs), which are extensions of the common non homogeneous Poisson process (NHPP)-based SRMs, and describe the probabilistic behavior of software fault-detection process by incorporating the time-dependent software metrics data observed in the development process. Especially we generalize the seminal PI-SRM in Rinsaka, Shibata and Dohi (2006) by introducing eleven well-known fault-detection time distributions, and investigate their goodness-of-fit and predictive performances. In numerical illustrations with four data sets collected in real software development projects, we utilize the maximum likelihood estimation to estimate model parameters with three time-dependent covariates; test execution time, failure identification work and computer time-failure identification, and examine the performances of our PI SRMs in comparison with the existing NHPP-based SRMs without covariates. It is shown that our PI-STMs could give better goodness-of-fit and predictive performances in many cases.

A new discrete distribution for count data called extended biparametric Waring (EBW) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring (UGW) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the UGW distribution, the EBW can model both overdispersed and underdispersed data sets. In fact, the EBW distribution is a particular case of a UWG distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson (CTP) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the UGW model. We compare the EBW with the UGW by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.