Computer Science and Mathematics

Abstract: Understanding tourist behaviour requires analytical frameworks capable of capturing both symmetric relationships among motivational constructs and asymmetric causal effects on behavioural intentions. Conventional segmentation approaches, particularly those based on structural equation modelling, primarily estimate directional relationships and provide limited insight into the multivariate interaction structures underlying tourist decision-making. To address this limitation, this study proposes an integrated analytical framework that combines GH-Biplot, Co-Inertia Analysis (COIA), STATICO, and Neutrosophic Psychology to analyse tourist motivations under uncertainty. The proposed framework was applied to a sample of 400 tourists participating in poverty-reducing tourism research. Measurement models were validated using confirmatory factor analysis and Partial Least Squares Structural Equation Modelling (PLS-SEM), while the proposed multivariate approach was employed to identify latent symmetric and asymmetric structures linking behavioural intentions, motivational constructs, and personal values. Results show that biospheric values exhibit the strongest association with intentions to participate in poverty-reducing tourism. More importantly, the proposed framework reveals multivariate relationships and behavioural patterns that remain hidden when conventional asymmetric causal models are applied independently. The incorporation of neutrosophic psychology further extends the analysis by explicitly representing indeterminacy in tourist motivations through truth, falsity, and indeterminacy components. The study contributes by introducing a novel analytical framework that integrates complementary multivariate techniques to improve tourism segmentation, enhance the interpretation of complex behavioural relationships, and support evidence-based decision-making for sustainable tourism management under uncertainty.

Abstract: In satellite and space debris laser ranging, photon-counting time-of-flight sequences exhibit spatio-temporal echo coherence and deterministic orbital constraints. We propose an unsupervised framework exploiting this spatial-kinematic coupling to extract weak returns under high background noise. First, a fuzzy clustering regression employs a dynamic energy functional and cross-entropy-regularized photon attribution, guided by target motion priors. To enhance low signal-to-noise ratio sensitivity, we introduce a low-gradient sampling strategy that theoretically guarantees a signal-to-background ratio exceeding 1/2. Furthermore, a dual-stream autoencoder fuses orbital kinematic parameters and multi-scale echo densities via noise-adaptive latent gating. Validation on 88 satellite and 24 debris datasets achieves F1-scores of 0.73 and 0.93, respectively. The sampling strategy reduces computational latency by ∼5.2% with no loss in tracking precision. This label-free, physically grounded approach enables robust weak signal detection in ground-based photon-counting lidar.

Abstract: This paper identifies and characterizes the Background Driving L\'evy Process (BDLP) associated with the Generalized Tempered Stable (GTS) distribution, a flexible seven-parameter family of infinitely divisible distributions with applications in physics and quantitative finance. We show that the corresponding BDLP is a finite-variation, infinite-activity Type B L\'evy process and derive its cumulants.

Abstract: The concept of ranked sparsity, originally introduced in the context of penalized regression, arises in modeling applications when an expected disparity exists in the quality of information between different feature sets. Its presence can cause traditional and modern model selection methods to fail because such procedures commonly presume “covariate equipoise” — that each potential parameter is equally worthy of entering into the final model. However, this presumption does not always hold, especially in the presence of derived variables or with highly disparate feature sets (i.e., multi-modal data). For instance, when all possible interactions are considered as candidate predictors, the sheer number of them grossly inflates the number of false discoveries, resulting in unnecessarily complex and difficult-to-interpret models with many (truly spurious) interactions. In this work, we motivate a ranked sparsity extension to the Bayesian Information Criterion (RBIC) that requires a stronger level of evidence in order to allow certain variables (e.g. interactions vs main effects and genetic vs clinical covariates) into a model. We compare the performance of RBIC relative to competing methods for selecting polynomials and interactions in a simulation study and in two applications, showing that stepwise selection guided by RBIC produces better-predicting, more transparent models (with fewer false interactions) compared to existing alternatives.

Abstract: Obesity is a major problem worldwide, particularly in Latin countries such as Mexico, Peru and Colombia. This study aims to evaluate five models (XGBoost, Random Forest, Multinomial Logistic Regression, Linear Discriminant Analysis (LDA) and Support Vector Machines (SVM)) from the statistical and machine learning fields to determine which of them is the most effective in classification of obesity levels in a multivariate classification model. The research uses a dataset of 2111 records consisting of 17 physiological and behavioral attributes which had to be preprocessed, such as one-hot encoding and multicollinearity filtering, and a powerful 10-fold cross validation methodology. It is shown that the results of ensemble methods are much better than those of the traditional parametric ones. XGBoost achieved the highest classification accuracy (97.54%), and an F_1-score of 0.9747, while Random Forest achieved the 2nd highest classification accuracy (95.64%). For all comparisons, McNemar's pairwise significance tests validated the superiority of XGBoost (with p<0.0001). Feature importance analysis was used to determine the most significant features as follows: weight, height, age and number of vegetables consumed per week (FCVC). While the study showcases the power of gradient boosting for capturing non-linear interactions in health data, the exclusive use of synthetic data (77% from SMOTE) poses drawbacks as it may overestimate performance and limit generalizability. The proposed ensemble architectures should be further evaluated on larger, all-nonsynthetic datasets to be clinically generalizable in the future.

Abstract: I give estimates of low bias for functions of moments. Let \( F(x) \)be a distribution on \( R^s \). Let \( F_n(x) \) be the empirical distribution of a random sample of size \( n \) from\( F(x) \). Given a functional \( F(x) \), \( E\ T(F_n) \)estimates \( T(F) \)with bias \( \sim n^{-1} \). (The bias is zero for a mean, but this is the exception.) The jackknife and bootstrap estimates only reduce this bias to \( \sim n^{-2} \), and are computationally intensive. I review the main two analytic methods to obtain an estimate of \( T(F) \) of bias \( \sim n^{-k} \)for \( k\leq 4 \)in terms of the functional derivatives of \( T(F) \). I give a chain rule for these derivatives when \( T(F)=g(U(F)) \) and \( g:R^q\rightarrow R \)is any given smooth function with finite partial derivatives at \( U(F)\in R^q \). I apply this to give an estimate of \( T(F) \) of bias \( \sim n^{-k} \)for \( k\leq 4 \), in terms of the derivatives of \( g \)and \( U(F) \). Examples include moment estimates and maximum likelihood estimates.

Abstract: There has been significant interest in the quantification of statistical evidence. This paper presents a statistical philosophy focused on quantifying statistical evidence derived from data, rather than following the traditional approach of presenting statistical methodology. Our focus will be on the reasoning underlying the methods, offering a fresh development of several familiar statistical approaches. We will also illustrate how a simple example requires considerably more detail. Our paper explores additional questions that analysts should pursue. We examine issues related to the determination of sample size, stopping rules, multiple hypotheses, and how effect sizes impact the quantification of statistical evidence.

Abstract: A novel axiomatic foundation of entropy has recently been proposed overcoming the limitations of classical and information-theoretic entropy foundations and eventually unifying probabilistic and physical entropy. A new set of postulates leads to a rigorous, uncertainty-based definition of entropy consistent with the principle of maximum entropy. Entropy is thus a purely stochastic concept quantifying uncertainty, thereby completing Kolmogorov’s probability system. Applied to gas thermodynamics, the new framework reproduces classical results and derives, rather than assumes, the laws of thermodynamics. In atmospheric applications, entropy maximization yields an isothermal state as the molecular equilibrium. Gravitation does not alter the isothermal state but distinguishes it from the isentropic one of macroscopic air parcels, whose motion drives the atmosphere away from equilibrium. Radiatively active gases, through interactions with shortwave and longwave radiation, sustain non-equilibrium vertical profiles of the atmospheric variables. Combined with the Stefan-Boltzmann law, these mechanisms provide a simple, parsimonious and coherent explanation of observed atmospheric behaviours and the climatic system. The framework highlights thermodynamics as emergent from stochastics, offering new insights into molecular uncertainty, emergence of macroscopic structures and radiation in shaping Earth’s climate. It also suggests a broader stochastic view of nature and atmospheric processes.

Abstract: Classical moment theory constitutes one of the fundamental pillars of probability and statistics, providing quantitative measures of location, dispersion, skewness, and higher-order characteristics of probability distributions. However, many contemporary problems in statistics, machine learning, finance, engineering, and data science involve nonlinear transformations of random variables, for which ordinary moments may not adequately capture the underlying stochastic behavior. This motivates the study of functional moments, defined as expectations of powers of transformed random variables. This chapter develops a comprehensive theoretical framework for functional moments of Gaussian random variables and introduces the concept of the Functional Moment Generating Function (FMGF), which serves as a unified generating mechanism for all functional moments. Beginning with a general formulation of functional moments, exact infinite-series representations are derived using Taylor expansions and the central moments of Gaussian distributions. These representations lead naturally to operator formulations, asymptotic approximations, Jensen-type inequalities, derivative-based bounds, Hölder inequalities, Lyapunov inequalities, and Lipschitz-type estimates. The chapter further introduces functional cumulants through the logarithm of the FMGF and establishes their relationship with transformed stochastic processes. Several numerical investigations involving polynomial, exponential, logarithmic, trigonometric, and logistic transformations are presented to illustrate the theoretical results. Comparative studies between exact functional moments and Taylor-series approximations demonstrate the accuracy and computational efficiency of the proposed framework. To highlight practical relevance, five real-world applications are examined, including uncertainty propagation in machine learning activation functions, reliability assessment in engineering systems, expected utility analysis in financial mathematics, nonlinear signal processing, and environmental risk modelling. Numerical examples, simulation studies, tables, and graphical illustrations are provided throughout the chapter. The proposed framework extends classical moment theory to a substantially broader setting and provides a unified methodology for studying nonlinear transformations of Gaussian random variables. Several future research directions are discussed, including multivariate functional moments, dependence-aware functional moment generating functions, functional cumulant theory, high-dimensional asymptotics, and applications in modern statistical learning.

Abstract: Healthcare continuous data often deviate from normality, which can substantially increase the risk of making invalid inferences, given that many inferential statistical procedures rely on normality assumption. To obviate this issue, we propose a new family of non-normal distributions based on a linear combination of the quantile functions of standard logistic and uniform (0, 1) distributions. This new family of non-normal distributions is characterized by using the methods of L-moments, conventional moments, and percentiles. Its performance is compared among the three methods in the context of parameter estimation and data modeling. The results of Monte Carlo simulation and bootstrapping techniques indicate that the L-moment-based estimates of parameters of L-skewness and L-kurtosis are substantially less biased than their percentile-based estimates of left-right tail-weight ratio (a measure of skewness) and tail-weight factor (a measure of kurtosis), which in turn are superior to their moment-based counterparts of skewness and kurtosis, especially for small sample sizes and higher-order moments. On the other hand, the data modeling results indicate that the percentile-based fits of the proposed distributions provide slightly better approximations to real-world healthcare data than their L-moment-based counterparts, whereas both percentile- and L-moment-based methods are superior to their conventional moment-based counterparts.

Abstract: Institutional distrust is treated here not as a low value of trust but as a positive social disposition, the settled expectation that formal procedures and official explanations no longer carry their stated public meaning. The paper studies the consolidation of that disposition as a threshold event. Building on a stochastic trust-phase model, it applies the same multiplicative-noise mechanism to a delegitimating assertion, so the bounded state variable is the probability of adopting institutional distrust. A logit transformation maps the inherited nonlinear diffusion exactly onto Brownian motion with drift and yields closed-form first-passage formulas for the crossing of operational distrust thresholds. The endpoints of the bounded variable are limiting consolidated regimes rather than finite-time targets, so observable institutional failure is threshold passage and not literal absorption at zero trust. The drift-to-turbulence ratio fixes the shape of the crossing probabilities and the noise scale fixes the time scale. The same coordinate measures the distance between social layers facing one assertion. In United States partisan survey data this inter-layer logit distance is large and, on consolidated assertions, stationary, the empirical signature of a completed passage, while valence assertions reset with the change of incumbent.

Abstract:

Let \(X = \left( X_{t} \right)_{0 \leq t \leq T}\) be a real-valued continuous process. For a threshold \(a\), the sub-threshold time set \[E_{T}(a) = \{ t \in \lbrack 0,T\rbrack:X_{t} \leq a\}\] encodes several different threshold observables. The most elementary one is the cumulative occupation time \[A_{T}(a) = \int_{0}^{T}\mathbf{1}_{\{ X_{t} \leq a\}}\, dt.\] For a regular one-dimensional diffusion, the classical occupation density formula gives \[A_{T}(a) = \int_{- \infty}^{a}\frac{L_{T}^{y}(X)}{\sigma^{2}(y)}\, dy,\] and hence \[\frac{\partial A_{T}}{\partial a}(a) = \frac{L_{T}^{a}(X)}{\sigma^{2}(a)}.\] Thus additive threshold occupation admits a local-time sensitivity calculus. In the terminology of barrier contracts, this additive clock is the cumulative, non-resetting Parisian clock, also called the Parasian clock. The purpose of this paper is to contrast this additive/Parasian regime with the behavior of resetting Parisian burst functionals. The connected components of \(E_{T}(a)\) represent sub-threshold episodes. We study in particular the longest burst \[M_{T}(a) = \sup\{|I|:I\text{ is a connected component of }E_{T}(a)\}.\] While \(A_{T}\) is locally controlled by local time, \(M_{T}\) is governed by the connectivity of the sub-threshold time set. We prove that \(M_{T}\) is monotone, that its supremum is attained, and that the weak-sublevel version is right-continuous with left limits, while the strict-sublevel version is its left-continuous regularization. The jump at a level is the increase in the maximal connected-component length produced by adjoining the level set. This gives a deterministic càdlàg/càglàd calculus for longest-burst profiles. For regular one-dimensional diffusions, this yields a sharp structural contrast. At deterministic levels which are almost surely not local-extreme values, the weak and strict longest bursts agree almost surely. Whenever the path has a unique interior maximum, the level-indexed longest-burst profile has a positive jump at the maximum level and is therefore not absolutely continuous. Brownian motion satisfies this criterion almost surely. We further identify the deterministic mechanism behind this instability: small threshold increases may fill short temporal bridges and merge large sub-threshold components. Finally, we show that the longest burst is exactly a one-sided continuous Parisian functional. This yields an exact Laplace-transform representation of its Brownian law through the Chesney--Jeanblanc-Picqué--Yor [1] Parisian transform, and an excursion-measure formulation in which local time enters only as the Itô excursion intensity. We also discuss smoothed burst statistics, moving thresholds, and diffusion examples. The paper is intended as a threshold-sensitivity comparison: local time controls cumulative Parasian occupation, whereas resetting Parisian burst observables are controlled by component mergers and excursion structure.

Abstract: Evaluating joint predictive performance for multivariate hydroclimatic models requires metrics that simultaneously assess marginal accuracy and cross-variable dependence recovery. Existing metrics – the Energy Score, Variogram Score, and their derivatives – do not adapt to the structural complexity of the residual correlation matrix, treating a single correlated pair identically to a fully dense dependence structure. We propose two novel metric families: Metric~E (E-CVWMD: Enhanced Coefficient-of-Variation Weighted Marginal-Dependence) and Metric~E2 (E-CVWMD-Pairwise), designed for mixed-type multivariate responses combining continuous and binary outcomes within a cross-validation framework. We position Metrics~E and~E2 as diagnostic ranking tools for comparing competing models rather than as strictly proper scoring rules, and we provide a strictly proper Log-Loss variant (E-LL / E2-LL) for applications that require the full properness guarantee. Metric~E assigns variable-level weights proportional to the coefficient of variation (CV) of each outcome on the training partition, and adaptively calibrates the marginal-dependence trade-off parameter $\alpha^*$ via a global distance-correlation test. Metric~E2 refines this by replacing the global test with a pairwise Spearman screening index $\hat{\pi}$ – the proportion of variable pairs with significant residual correlation – which maps linearly to $\alpha^*(\hat{\pi}) = 1 - \hat{\pi}/2 \in [0.5, 1]$. Applied to the validation of a Generalized Multivariate Functional Additive Mixed Model (GMFAMM) on 62 Valle del Cauca meteorological stations ($N_{\text{test}} \approx 31\,663$), the naive significance-based index saturates ($\hat{\pi} = 1.0$) at this large sample size – every pair, including correlations as small as $|\hat{\rho}_s| \approx 0.01$, is flagged ``significant'' – which is precisely the sample-size sensitivity we address. Under the effect-size screening ($|\hat{\rho}_s| \geq 0.05$), three negligibly correlated pairs are excluded, yielding $\hat{\pi} = 0.70$ and $\alpha^*_{E2} = 0.65$, a better-calibrated weight than Metric~E's $\alpha^*_E \approx 0.797$ under the same data. A large-scale simulation study with 37,440 model evaluations confirms that Metric~E inverts the correct ranking at correlation levels $\rho \geq 0.40$ (CDR = 0\%), while E2 maintains correct discrimination in 14 of 15 simulation conditions (M1 vs. M3). We also delimit the metrics' scope: E2 degrades under near-saturated uniform dependence – a regime in which the strictly proper Energy Score remains preferable – and the pairwise index is sensitive to sample size, for which we provide an effect-size-based variant. An R package (mvmetrics v0.2.0, https://darango2025.github.io/mvmetrics) implementing both metrics, the Log-Loss variant, alternative weighting schemes, and the effect-size screening is publicly available.

Abstract: This paper proposes a new four-parameter statistical distribution based on the neutrosophic Gompertz (NGo-G) family and the extended Nadarajah-Haghighi distribution in neutrosophic logic called neutrosophic Gompertz Nadarajah-Haghighi (NGoNH) distribution to deal with uncertain and indeterminate data, known as neutrosophic data. The basic distribution functions and some properties are derived and the parameters of the proposed distribution are estimated using three different methods. To compare the performance of the different estimation methods, numerical simulations are performed using the evaluation criteria: MSE, RMSE, and bias. NGoNH distribution is applied to real data set representing the monthly minimum and maximum temperatures in Lahore, Pakistan, for the period 2016-2020. To verify the consistency of the data with the proposed distribution, the properties of the neutrosophic data are tested and the three components (True, Indeterminate, False) are plotted. In addition, the performance of the proposed distribution is compared with six other neutrosophic distributions using some information criteria and some goodness-of-fit tests. The extent to which the data fit the proposed distribution is plotted to demonstrate its effectiveness. The results indicate that the proposed distribution provides a better fit to neutrosophic data than other distributions, which enhances its effectiveness in analyzing data with uncertainty.

Abstract: We consider the problem of optimal linear estimation of the functional A_Nξ = ∑^N_k=0 a(k)ξ(k) which depends on the unknown values ξ(k), k = 0,1,...,N, of a stochastic sequence with harmonizable symmetric α-stable nth increments. The derived estimates are based on observations at points m ∈ Z \ {0,1,2,...,N}. The cases of observations without noise, with harmonizable symmetric α-stable noise and with noise having harmonizable symmetric α-stable increments are studied. The classical solutions as well as the minimax robust ones are obtained.

Abstract: The Poisson–Three-Parameter Lindley (PTPL) distribution constitutes a flexible Poisson mixture model for overdispersed count data, encompassing several classical count distributions as special or limiting cases. Despite its growing use in applied contexts, no formal goodness-of-fit test specifically designed for this distribution is currently available. In this paper, we propose and study a new goodness-of-fit test for the PTPL model based on a Cramér-von Mises type distance between the empirical and theoretical probability generating functions (PGFs). For polynomial weight functions, the test statistic admits an explicit closed-form representation; in practice, it is computed efficiently via numerical quadrature. The null distribution of the statistic is approximated via parametric bootstrap. We establish theoretical properties of the proposed procedure, including consistency against fixed alternatives and the validity of the bootstrap approximation. Monte Carlo simulations with sample sizes n ∈ {50,100,150,200,500} for size evaluation and n = 250 for power comparisons, and weight exponents a ∈ {0,1,2}, show that the empirical size is well controlled at both the 5% and 10% nominal levels, and that the test exhibits competitive power against Poisson, Negative Binomial, COM-Poisson, and Zero-Inflated Poisson alternatives. Areal data application to five overdispersed count datasets further illustrates the practical utility of the method.

Abstract: Wedocument anetwork-level vulnerability in pension fund systems: lifecycle allocation regulation, designed to protect individual participants, compresses cross-fund return dynamics to the point where provider choice offers little diversification. Using daily net asset value data from second-pillar pension funds in Lithuania over 2019–2025, we find that a single common factor explains at least 73% of total return variance even in the calmest observed periods. We develop an unsupervised regime-detection framework combining a PCA-based absorption ratio, DTW hierarchical clustering, and a Gaussian hidden Markov model with a data-driven crisis threshold. The HMM specification is supported by a dual empirical calibration of the stickiness prior and cross-validated against a fully Bayesian sticky HMM. The framework identifies three latent regimes in which elevated systemic co-movement is the structural norm rather than an exceptional state and shows that funds group primarily by age cohort rather than by provider. The absorption ratio has no significant relationship with global equity benchmarks in either calm or high-risk regimes, indicating that systemic stress is network-internal rather than imported. Cluster-level tracking-error amplification of 1.09× to 1.23× during high-risk episodes confirms that even conservative funds serving retirement-age participants are not insulated.

Abstract: This article critically examines Jack Duffield’s proposition that (all) intelligence analysts should become competent in “a core set of statistical analytical techniques” so as to address the “total information overload” they have experienced following the proliferation of ‘Big Data’. It summarises the generic (technique-agnostic) and particular (technique-specific): analytical choices and decisions that analysts need to be competent to make when using each of the 11 techniques proposed; together with the parametric and non-parametric assumptions on which each of these techniques rely; the sources of non-systematic and systematic error that analysts using these techniques need to address; and the diagnostic measures that providers and consumers of findings generated by these techniques should use to assess any flaws or contingencies associated therewith, and thereby temper any associated inferential certainty and importance. When compared to baseline statistical competencies of non-specialist intelligence analysts, these summaries demonstrate the substantial additional training that Duffield’s proposition would require. The article concludes that this may prove a big ask without an extended period of additional training, work-based experience and specialist supervision. In the absence thereof, underqualified intelligence analysts using such techniques would risk undermining intelligence analyses with multiple analytical and inferential mistakes.

Abstract: Stochastic computing represents numerical values as probabilities encoded in Bernoulli bitstreams, enabling simple logic-based operations but also introducing practical challenges related to bitstream length, correlation, synchronization, and scalability. These challenges become especially important when heterogeneous physical signals are processed directly by mapping each low-level feature into a separate stochastic stream. This work proposes a hierarchical event-oriented stochastic processor architecture for continuous monitoring of event probabilities. Instead of directly encoding all physical signal features as independent bitstreams, the proposed architecture introduces local event-probability formation blocks. Each local block converts task-relevant features of a physical channel into a compact set of calibrated or model-defined event probabilities, which are then represented by Bernoulli bitstreams and processed by a stochastic event-fusion core. The processor output is not a single static decision value but a time-resolved global event-probability signal, P_event (t), enabling temporal analysis of event persistence, repetition, trend, and accumulated exposure. As a proof of principle, the architecture is demonstrated using a synthetic acoustic monitoring scenario. Acoustic features associated with warning-like, repeated, prolonged, impact-like, and background sound patterns are converted into local event probabilities and subsequently into stochastic bitstreams. The results show that the proposed hierarchical representation can reduce the number of required stochastic streams while preserving event-level interpretability. The numerical demonstration also illustrates the expected compression–accuracy trade-off: direct feature-to-bitstream mapping may provide lower reconstruction error, whereas hierarchical event mapping improves architectural compactness and supports continuous event-level monitoring. The proposed framework provides a basis for future optical, photonic, or hybrid implementations of event-oriented stochastic processors for probabilistic sensing and decision-support systems.

Abstract: This paper studies an optimal consumption-investment problem in a multi-asset financial market where risky assets returns incorporate returns history. Preferences are modelled using Epstein-Zin recursive utility, allowing a separation between risk aversion and intertemporal substitution. Using the well-known martingale optimality principle and forward-backward stochastic differential equations (FBSDEs), we obtain explicit closed-form solutions for the optimal strategy and value function. A sensitivity analysis illustrates the dependence of optimal policies and value function on key parameters, including risk aversion, elasticity of intertemporal substitution (EIS), memory horizon, learning intensity, and wealth-history parameters. The findings provide new insights into the interaction between behavioural features and dynamic portfolio choice in a multi-asset setting.