What ‘Typical Insights’ Might ‘Core Statistical Analytical Techniques’ Provide to Intelligence Analysts?

1. What Choices/Decisions Must Analysts Make When Using the 11 Techniques?

A non-exhaustive list of the generic (technique-agnostic) and particular (technique-specific) choices and decisions analysts must (be competent to) make when using any of the 11 techniques Duffield (2026) proposed, have been summarized in Table A1.1, Table A1.2 and Table A1.3 (see Appendices). In the main, the choices/decisions summarised in Table A1.1 and Table A1.2 focus predominantly on design- and dataset-related considerations, each of which should themselves be determined in line with the ‘analytical objective’ – i.e. with the choice/decision made as to the intended application of the analyses concerned, be these for descriptive, ‘predictive estimation’, optimisation or causal inference purposes. All of these overarching analytical objectives benefit from datasets that offer a representative sample of all ‘cases’ (i.e. the ‘population’) to which their analytical findings can then be applied – be this a ‘population’ of entities, events, processes, or characteristics thereof. However, for ‘predictive estimation’ and optimisation objectives,² the principal benefit of representative datasets is that the ‘predictive estimation’ and optimisation algorithms generated will be broadly generalisable to all other similarly representative datasets elsewhere. However, where only unrepresentative datasets are attainable/available, useful ‘predictive estimation’ and optimisation algorithms can still be usefully generated, though only for subsequent application to similarly unrepresentative datasets – including the original dataset concerned, or any other comparable datasets that have been sampled/selected in a similarly unrepresentative fashion – such that they contain sufficiently similar distributional properties on which the algorithms generated can operate faithfully.

The remaining choices and decisions within Table A1.1 and Table A1.2 fall into those concerned with: the size of the sample required to support the analyses and insights intended, and the levels of precision required; what specific variables the dataset needs to contain; how these variables need to be prepared/processed prior to analysis; and what diagnostic measures/settings are required to optimise the accuracy, precision and interpretability of the resulting analytical findings (and any insights that might be inferred therefrom). In this regard, irrespective of the analytic objective intended, it is crucial that:

• the number of ‘cases’ (i.e. ‘population’ members) on which measurements are available is sufficient to both: support the analytical techniques applied; and reduce the risk of the findings being subject to chance effects (i.e. non-systematic error);
• measurements are available on all cases for all variables pertinent to (and required for) the sample- and variable-dependent analyses intended (and that any under-/over-represented cases can be dealt with, where necessary/appropriate, using robust weighting variables; and any missing values can be accurately imputed – and not least when missing cases/values are not missing [completely] at random, and therefore risk undermining the representativeness of the dataset); and
• these variables include not only the specified ‘target’ variable (for ‘predictive estimation’ and optimisation objectives) or ‘outcome’ variable (for description and causal inference objectives), but also a sufficiently varied array of covariates/predictor variables so as to optimise the diversity of statistical information required to: strengthen the accuracy and precision of the estimated dataset features (for ‘predictive estimation’ and optimisation objectives); and adjust for potential confounders (for causal inference purposes).

Deciding how many measurements, and of which variables, are necessary to collect (or need to be present within the secondary dataset selected), can prove an uncertain art and statistically challenging to operationalise – particularly when there is limited time and resource available to generate datasets that meet/exceed the ‘optimum’ size and diversity desired; or when the secondary datasets available do not contain either the number of measurements or range of variables desired. In such instances – which are commonplace in real world settings – the analysts concerned will need substantial skill to balance the benefits of sample size over diversity (notwithstanding representativeness) when compiling or selecting the datasets they use. They also need to be able to: judge when the size and/or diversity of the dataset required for their intended analytical objective is not achievable/available; and assess whether it is better to step back from attempting to achieve their desired/intended analytical objective using datasets that are patently incompatible with doing so confidently (or, at least, without a substantive risk of excessive imprecision and/or bias).

Meanwhile, even those datasets that do contain sufficient measurements from sufficiently diverse variables may require these data to be carefully pre-processed so as to: optimise the variance-determined statistical information available for use by the analytical technique(s) concerned; and facilitate the interpretation (and communication) of any findings generated. This includes not only procedures to address missing values (as mentioned earlier), but also – subject to the assumptions required by the analytical technique applied (see Section 2, below) – any necessary transformation of the raw data into meaningfully ordinal or categorical variables, and to normalise and/or linearise the distribution of their measurements/variances and/or model residuals. Overlooking or misjudging these considerations can lead to imprecise, inaccurate, unreliable and invalid findings; or findings that are unnecessarily challenging to interpret or explain to non-specialist consumers of the insights produced. Again, these decisions require great care and thoughtfulness so as to: not simply ensure that the sampling, precision, linearity and/or distributional requirements are met; but also to hold fast to the intended/desired analytical objective and the inferential needs of their customers.

Finally, aligning the diagnostic measures selected for testing and evaluating the integrity of the analyses³ with the size and diversity of the dataset available, the analytical technique selected, and the intended analytical objective, is also an important consideration. This is particularly the case when weaknesses in any of these analytical components, or a lack of firm empirical knowledge and/or theoretical understanding, increase the extent of analytical uncertainty and thereby reduce analytical confidence. Such measures need to be fit for purpose if they are to challenge the integrity of the analyses and offer confidence that their findings can survive such testing/evaluation, and can therefore be considered robust.

These (technical) considerations come more to the fore in Table A1.2 (summarising the technique-agnostic choices/decisions that are particular to Duffield’s (2026) 11 proposed statistical analytical techniques) and Table A1.3 (summarising the technique-specific choices/decisions that are particular to smaller subsets – and occasionally just one – of these 11 techniques). Together these illustrate the depth of technical knowledge and expertise required to competently apply each and every one of these 11 statistical analytical techniques – knowledge and expertise that goes some way beyond the more generic quantitative analytical competencies summarised in Table A1.1.

2. What Parametric/Non-Parametric Assumptions Need Apply When Using the 11 Techniques?

The generic (technique-agnostic) and particular (technique-specific), parametric and non-parametric assumptions that should apply when using each of Duffield’s (2026) 11 proposed techniques have been summarised in Table A2.1 and Table A2.2, respectively (see Appendices). The first of these, for the most part, comprise assumptions that commonly apply to a far wider range of statistical techniques – these being those related not only to the analytical objective (and the constraints this can impose on the objective function/loss criterion modelled), but also to:

• the representativeness/external validity of the dataset used;
• the reliability and internal validity of the measurements taken/available on each of the variables therein;
• the appropriateness of the data type, scaling and transformation(s) adopted for/applied to these variables – particularly as required for the statistical technique concerned;
• the independence of measurements/observations made for each of the dataset’s/sample’s individual ‘cases’/’population’ members;
• the absence (or appropriate treatment of) extreme (‘outlier’) measurements/observations;
• the appropriateness of the size of the dataset/sample, and any necessary randomness assumptions (where relevant to re-/sub-sampling procedures germane to the statistical technique applied); and
• a sound theoretical understanding of the temporal sequence of variables – particularly for modelling time-dependent relationships/associations (such as causal pathways).

As such, these assumptions add to many of the dataset- and data-related choices/decisions that analysts need to (be competent to) make when using any (or at least most) statistical techniques – as summarised in Section 1 (above), and in Table A1.1 and Table A1.2. As such, these comprise a broader corpus of considerations and obligations that analysts need to understand and apply whenever they attempt (m/any) statistical analytical techniques.

However, the more particular (technique-specific) assumptions that need to apply (predominantly, though not necessarily exclusively) to each of Duffield’s (2026) 11 proposed techniques – as summarised in Table A2.2 – are substantively different to the parallel choices/decisions contained in Table A1.3. Though some of these assumptions determine what choices/decisions analysts must make when designing, implementing and interpreting the results generated by these techniques, most relate to more granular technical issues that distinguish each technique as somewhat unique – and again speak to the depth of specialist knowledge, understanding and expertise that analysts require when applying these.

3. What Are the Potential Sources of Imprecision and Bias When Using the 11 Techniques?

The potential sources of non-systematic and systematic error (i.e. imprecision and bias) summarised in Table A3.1 and Table A3.2 (see Appendices) can occur at each and every stage of any (statistical) analytical process – from design, sampling and measurement through to analysis, interpretation and implementation. They are also evident in any flaws in the design and application of the specific (statistical) analytical process concerned, and in any knock-on consequences of the interpretations made and inferences drawn from their apparent (yet misinterpreted) findings. Arguably, each of these flaws primarily occurs as a result of mistaken choices/decisions or violated (overlooked/untested) assumptions amongst those summarised in Table A1.1 through Table A2.2 (see Section 1 and Section 2, above). This is because imprecision and bias are in no small part the result of poor (statistical) analytical practice, and as such are a prominent feature of the problems that can arise when analysts with inadequate knowledge, understanding and expertise attempt to apply (and interpret findings generated by) these techniques without recourse to specialist guidance, advice, supervision and support.

Yet the very existence, importance and potential consequences of a good many of the sources of imprecision and bias summarised in Table A3.1 – and even more so for those summarised in Table A3.2 – remain somewhat contentious and contested amongst qualified and experienced statistical professionals. As a result, many are widely overlooked or ignored in what passes for contemporary professional statistical practice (or the canonical works consulted when preparing Table 1, above). In part this reflects the differing pace of discovery and change in the fields of theoretical (or ‘classical’) statistics, and the more applied and contextually cognisant discipline of ‘biostatistics’ – in which the latter faces more frequent opportunities for identifying unacknowledged flaws in accepted techniques through their use in novel data-centric problems, contexts and expectations. This has two consequences for the wider application of statistical analytical techniques by intelligence analysts:

• First, that many ‘standard’ techniques may prove less applicable to the data and datasets that are available, and of most interest, to intelligence practitioners and their customers; and
• Second, that these data/datasets are likely to pose novel statistical challenges to many of the more commonly used statistical analytical techniques.

Examples of the former include the greater number and importance of predominantly unprecedented, singular phenomena/events amongst those that constitute “priority intelligence requirements” (PIRs; MOD, 2023) – phenomena/events for which, and on which, there is often a dearth of comparable past measurement/observation amenable to statistical analysis.⁴ As for examples of the second, in the absence of opportunities for controlled experimentation (which may nonetheless exist within some disciplines and domains, such as OSINT and CEMA; MOD 2023; 2024), the mechanistic understanding required for causal inference and foresight – as opposed to the estimation of unmeasured/unobserved future dataset features achieved using ‘predictive analytics’ – must rely entirely on careful consideration of temporality, and relentless efforts to address confounding bias while avoiding conditioning on variables acting as ‘colliders’ (Ellison, 2023). This is because only variables that occur (or crystalise in the form and value as, and when, measured/observed) after other variables can be plausibly considered their potential consequences; and only variables that occur (or crystalise) before other variables can be plausibly considered their potential causes.

Added to these is the inherent variability (and therefore intrinsic, if ultimately finite, unpredictability) of all life forms as a consequence of the intra- and inter-generational conservation of phenotypic and genotypic variability/diversity within changeable ecosystems that is central to the tenets of Darwinian natural selection. This is a relevant consideration in such contexts because these include the ‘extended phenotypes’ of human beings – as evident in the substantial diversity and ongoing diversification in perceptions, beliefs, ideas, understanding, explanations, interpretations, behaviours, cultures and artefacts – that each contribute ostensibly limitless sources of both non-systematic and systematic error (imprecision and bias) to all human-related intelligence concerns.

4. What Diagnostic Measures Should Producers of Statistical Analyses Use to Safeguard Their Methods?

As a safeguard against inappropriate choices/decisions, violated assumptions, imprecision and bias – and to evidence rigorous and robust statistical analytical practice – the routine application of a range of generic and specific diagnostic measures capable of identifying methodological concerns is gradually becoming inculcated into what passes for applied statistical doctrine (e.g. Lang and Altman, 2015; Ioannidis, 2017; 2019; Christensen et al., 2023; Hardwicke et al., 2023; Kim et al., 2024). As before, some of these diagnostic measures have broad utility irrespective of the statistical technique applied, while others predominately relate to less common features or peculiarities of the specific technique(s) involved. Non-exhaustive summaries of each – as relevant to the 11 techniques examined in this article – have been provided in Table A4.1 and A4.2 (see Appendices). In the main, both of these Tables include diagnostic measures that help identify whether the analysts concerned have:

• made appropriate choices and decisions when specifying/selecting their analytical objectives, statistical analytical designs, sampling frames/secondary datasets, measurement/observation protocols, analytical models and inferential interpretations – as summarised in Table A1.1, Table A1.2 and Table A1.3, and described in Section 1 (above);
• designed and conducted their analyses using analytical objectives, datasets, analytical models and inferences that comply with the assumptions required of all (or applicable principally to) specific statistical techniques – as summarised in Table A2.1 and Table A2.2, and described in Section 2, above; and
• applied great care to each of the (design-, sampling/selection-, measurement/observation-, analysis- and interpretation-related) steps involved so as to avoid, attenuate, mitigate, or acknowledge (and accommodate) all relevant sources of imprecision/bias (and thereby their consequences/effects) – as summarised in Table A3.1 and Table A3.2, and described in Section 3 (above).

As a result, there are few surprises amongst either the generic or specific diagnostic measures listed in these Tables given they relate to each of the choices/decisions, assumptions and sources of imprecision and bias that have already been described in preceding Sections of this article. What is nonetheless surprising are the number of additional procedures that competent analysts will need to have mastered to ensure their statistical analyses can be relied upon within the context of strategically, operationally and tactically critical intelligence analysis, fusion and assessment. The point being that far from it being sufficient for intelligence analysts to master the “basic”, “baseline” or “core” principles and techniques required to confidently analyse substantive quantitative/enumerable datasets (Duffield, 2026), they also need to know enough to: make good choices/decisions; pay attention to the assumptions on which the techniques they use depend; address (or acknowledge and accommodate) all potential sources of imprecision and bias; and critically evaluate their own analyses using diagnostic measures capable of identifying critical weaknesses, flaws, conditionalities or contingencies. This means that with statistical analytical techniques the burden of expertise is high, and – given: ongoing advances in methodological understanding; and in the technologies available for exposing (and addressing) some longstanding/newly discovered analytical flaws/weaknesses; and the diversification of datasets and questions to which these techniques are applied – all statistical analysts (and all statistically competent intelligence analysts) need to keep up with ongoing developments in professional practice.

5. What Alternative Interpretations/Inferences Might Each of Duffield’s 11 “Typical Analytical Insights” Support?

Taken together, the four preceding considerations (as examined in Section 1, Section 2, Section 3 and Section 4, above) set a high bar for the statistical expertise expected of intelligence analysts were they to take on additional statistical responsibilities – for collecting/sourcing, processing and analysing large quantitative (and enumerable) datasets; and applying robust diagnostic measures so as to evaluate and quality-assure their analyses – alongside their principal function as single/multi/all-source intelligence analysts. Added to this will be the skills required to – succinctly-yet-accessibly – explain to customers (including: juniors; peers; more senior colleagues; commanders; decision-makers… few of whom will have specialist statistical expertise): what inferences they have been able to generate from their analyses; and what evidence they have that any resulting insight/foresight might be considered both reliable and robust.

Neither of these skillsets are for the faint-hearted, nor for those who lack either the time or commitment required to: apply such techniques rigorously; and translate them assiduously for non-specialist audiences. Yet the confidence that comes from experience of using statistical methods – as with any other advanced/specialised technique – can substantively attenuate the scale of the work involved. This is because ‘statistical analyses’^1,4 are “not looking for perfection, but for advantage” (as the protagonist, George Smiley, described Steed-Asprey’s ‘double cross’ [XX] system in Le Carre’s celebrated 1974 novel, Tinker, Tailor, Soldier, Spy).

In statistical lore, a comparable and equally memorable aphorism can be found in the wise words of another George (George Box FRS – a much admired and distinguished statistician) who, at around the same time as Le Carre, wrote that “All [statistical] models are wrong, but some are useful” (Box et al., 1979). What both these Georges mean is that neither of these practices (be they: deception operations, for Smiley; or statistical inference, for Box) nor the techniques they use (be they: the ‘double cross’ [XX] system, for Smiley; or quantitative modelling, for Box) need to be mistake-, imprecision- or bias-free to be of potential tangible value/benefit to the problem at hand. Moreover, in an earlier article, Box (1976) had already set out what his (subsequently published) aphorism might mean for “scientists” – and by extension, for intelligence analysts and statistical analysts alike – namely that:

“Since all [statistical] models are wrong the scientist [statistician, or analyst] must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad.”

The relevance of this to Duffield’s (2026) proposition is that analysts who are committed to learning how to competently apply statistical analytical techniques will also learn, from practice and experience: which of the choices/decisions, assumptions, and sources of imprecision and bias pose the most important risks to the reliability, validity and substantive utility of their statistical analytical techniques; and which might only pose trivial concerns to the insights these techniques can provide.

The reason for labouring this point at this stage in the present article is to frame the scope of the critique that follows of the “typical analytical insights” Duffield (2026) drafted for each of his 11 proposed “statistical analytical techniques”. Since the detail provided in these “insights” was necessarily brief (given their intent, and the finite word count available to him within the confines of an academic journal article) they do not include the more detailed references to (m)any of the methodological and technical considerations explored in Section 1 through Section 4 (above) – information that might ordinarily be included in summaries of such findings within contemporary statistical publications/reports. As such, the critique that follows pays less heed to the absence of this more detailed methodological information, and instead assesses whether these (necessarily brief) examples of the “typical analytical insights”, that each of the 11 techniques are purported to able to provide, might:

• misrepresent what each technique involves or what findings it can provide; and thereby lead to the
• misinterpretation of what might properly be inferred from a more cautious summary of their findings.

These assessments, together with a more circumspect ‘alternative description’ of each “typical analytical insight”, have been summarised in Table 2, overleaf; and are described in more detail in Section 5.1 and Section 5.2, below.

Table 2. (part 1 of 3). An assessment of the potential methodological misrepresentation and inferential misinterpretation of the “typical analytical insights” Duffield (2026) drafted for each of the first 4 of the 11 “statistical analytical techniques” he proposed intelligence analysts should be competent to apply and interpret; together with alternative descriptions intended to attenuate the risk of misrepresentation or misinterpretation.

“Technique”	“Theme”	“Typical Analytical Insight”	Potential methodological misrepresentation	Potential inferential misinterpretation	Alternative description
Linear Regression	Regression	“After controlling for other variables, increases in X are consistently associated with proportional increases in Y, suggesting X is a meaningful driver rather than background noise.”	The thematic labelling of this technique is appropriate. Reference to “controlling for other variables” is appropriate, but only were the residual association between X and Y (after controlling for these specific “other variables”) be the intended/desired estimand.	The phrase “meaningful driver” implies that the association between X and Y can be confidently interpreted as consistent with X causing Y. This association is also consistent with: chance; reverse causality; collider bias; and unmeasured and/or residual confounding.	“X and Y are positively associated with one another after adjusting for all/all preceding* measured covariates.” *The inferential interpret-ability/-ion of the association depends upon which covariates were adjusted for, hence this warrants clarification.
Logistic Regression	Regression	“The probability of event A rises sharply once factors X and Y are present, indicating a threshold effect that distinguishes high-risk cases from the baseline.”	The thematic labelling of this technique is appropriate. Use of the term “probability” to mean ‘likelihood’, ‘rate’, ‘risk’ or ‘odds’ is potentially confusing. A “threshold effect” would require additional evidence of a more or less ‘stable state’ prior to an ‘inception point’ of some sort.	The phrase “threshold effect” risks misinterpretation as definitively causal (as in ‘cause and effect’). The increase in the odds of A in the presence of X and Y is also consistent with: chance; reverse causality; mathematical coupling; collider bias; and unmeasured and/or residual confounding.	“The odds that A occurs is positively associated with the presence of (both)* X and Y.” *Subject to clarification of the “typical analytical insight” as originally drafted
K-Nearest Neighbours	Classification	“This actor’s recent behaviour most closely resembles that of a small subset of previously observed cases, which historically went on to exhibit outcome B.”	The thematic labelling of this technique is appropriate. The use of the term “most closely resembles” is appropriate but its utility depends on which “recent behaviour[s]” were involved. The “small subset” of cases which exhibited “outcome B” suggests ‘conditioning on the outcome’ may have generated this association.	The phrase “historically went on to” risks misinterpretation as definitively causal. The elevated risk of “going on to exhibit outcome B” given the classification of the “actor’s recent behaviour” will also be consistent with: chance; reverse causality; collider bias; and unmeasured and/or residual confounding.	“(On the basis of the recent behavioural features measured)* This actor is most closely associated with past cases that later exhibited outcome B; but this actor’s risk of outcome B will depend upon the continuing presence of any other necessary factors/features.” *Subject to the limited scope of the behavioural features on which K-means classification was performed.
K-Means Clustering	Classification	“Observed entities naturally separate into four distinct behavioural groupings, each with internally consistent patterns and materially different risk profiles.”	The thematic labelling of this technique is appropriate. This analytical technique (alone) is not able to determine: how the groupings observed arise; the nature/extent of any “internally consistent patterns”; or group-related differences in “risk profiles”.	The use of “naturally separates into”, “materially different” and “risk profiles” infer a level of mechanistic understanding, substantive knowledge, and/or (additional) empirical analysis that lies beyond what this technique (on its own) can determine.	“(On the basis of the behavioural features measured)* Four distinct and internally consistent clusters were identified (and separate analyses indicate these clusters have different risk profiles for X [to be specified])” *Subject to the limited scope of the behavioural features on which K-means classification was performed.

Table 2. (part 1 of 3). An assessment of the potential methodological misrepresentation and inferential misinterpretation of the “typical analytical insights” Duffield (2026) drafted for each of the first 4 of the 11 “statistical analytical techniques” he proposed intelligence analysts should be competent to apply and interpret; together with alternative descriptions intended to attenuate the risk of misrepresentation or misinterpretation.

“Technique”	“Theme”	“Typical Analytical Insight”	Potential methodological misrepresentation	Potential inferential misinterpretation	Alternative description
Linear Regression	Regression	“After controlling for other variables, increases in X are consistently associated with proportional increases in Y, suggesting X is a meaningful driver rather than background noise.”	The thematic labelling of this technique is appropriate. Reference to “controlling for other variables” is appropriate, but only were the residual association between X and Y (after controlling for these specific “other variables”) be the intended/desired estimand.	The phrase “meaningful driver” implies that the association between X and Y can be confidently interpreted as consistent with X causing Y. This association is also consistent with: chance; reverse causality; collider bias; and unmeasured and/or residual confounding.	“X and Y are positively associated with one another after adjusting for all/all preceding* measured covariates.” *The inferential interpret-ability/-ion of the association depends upon which covariates were adjusted for, hence this warrants clarification.
Logistic Regression	Regression	“The probability of event A rises sharply once factors X and Y are present, indicating a threshold effect that distinguishes high-risk cases from the baseline.”	The thematic labelling of this technique is appropriate. Use of the term “probability” to mean ‘likelihood’, ‘rate’, ‘risk’ or ‘odds’ is potentially confusing. A “threshold effect” would require additional evidence of a more or less ‘stable state’ prior to an ‘inception point’ of some sort.	The phrase “threshold effect” risks misinterpretation as definitively causal (as in ‘cause and effect’). The increase in the odds of A in the presence of X and Y is also consistent with: chance; reverse causality; mathematical coupling; collider bias; and unmeasured and/or residual confounding.	“The odds that A occurs is positively associated with the presence of (both)* X and Y.” *Subject to clarification of the “typical analytical insight” as originally drafted
K-Nearest Neighbours	Classification	“This actor’s recent behaviour most closely resembles that of a small subset of previously observed cases, which historically went on to exhibit outcome B.”	The thematic labelling of this technique is appropriate. The use of the term “most closely resembles” is appropriate but its utility depends on which “recent behaviour[s]” were involved. The “small subset” of cases which exhibited “outcome B” suggests ‘conditioning on the outcome’ may have generated this association.	The phrase “historically went on to” risks misinterpretation as definitively causal. The elevated risk of “going on to exhibit outcome B” given the classification of the “actor’s recent behaviour” will also be consistent with: chance; reverse causality; collider bias; and unmeasured and/or residual confounding.	“(On the basis of the recent behavioural features measured)* This actor is most closely associated with past cases that later exhibited outcome B; but this actor’s risk of outcome B will depend upon the continuing presence of any other necessary factors/features.” *Subject to the limited scope of the behavioural features on which K-means classification was performed.
K-Means Clustering	Classification	“Observed entities naturally separate into four distinct behavioural groupings, each with internally consistent patterns and materially different risk profiles.”	The thematic labelling of this technique is appropriate. This analytical technique (alone) is not able to determine: how the groupings observed arise; the nature/extent of any “internally consistent patterns”; or group-related differences in “risk profiles”.	The use of “naturally separates into”, “materially different” and “risk profiles” infer a level of mechanistic understanding, substantive knowledge, and/or (additional) empirical analysis that lies beyond what this technique (on its own) can determine.	“(On the basis of the behavioural features measured)* Four distinct and internally consistent clusters were identified (and separate analyses indicate these clusters have different risk profiles for X [to be specified])” *Subject to the limited scope of the behavioural features on which K-means classification was performed.

Table 2. (part 2 of 3). An assessment of the potential methodological misrepresentation, and inferential misinterpretation of the “typical analytical insights” Duffield (2026) drafted for next 4 of the 11 “statistical analytical techniques” he proposed intelligence analysts should be competent to apply and interpret; together with alternative descriptions intended to attenuate the risk of misrepresentation or misinterpretation.

“Technique”	“Theme”	“Typical Analytical Insight”	Potential methodological misrepresentation	Potential inferential misinterpretation	Alternative description
ANCOVA (Analysis of Covariance)	Causal Inference	“Once baseline capability and environment are accounted for, the apparent gap between actors narrows significantly, indicating that much of the observed difference reflects starting conditions rather than divergent behaviour.”	The thematic labelling of this technique is inappropriate – ANCOVA is a ‘general linear model’ that can only identify associations between variables (but see below). Such associations can nonetheless support causal inference where they examine: focal relationships between preceding and subsequent variables; and after competently mitigating the risk of confounder and collider bias.	The original “typical analytical insight”, as drafted, presents only limited potential for inferential misinterpretation. The use of the phrase “narrows significantly” implies that the technique routinely provides a statistical measure of the similarity between ‘actor types’ (which it does not) and that this measure achieved a probability considered “significant”.	“The extent of the difference observed between different types of actors is substantively reduced following adjustment for baseline capability and environment, suggesting that much of the difference observed is due to their different starting conditions rather than subsequent developments”* *This is somewhat vague without information on what “differences” between actors were examined.
Trend Plotting	Time Series	“The underlying trajectory shows a sustained upward movement over multiple periods, with short-term volatility masking a longer term structural change.”	The thematic labelling of this technique is appropriate. The use of the phrase “structural change” may exceed the evidence (of ‘underlying mechanism’) this technique can provide – although this will ultimately depend upon what variables/features have been modelled in this analysis.	There is a risk that the phrase “structural change” may encourage solely those inferences that focus on (structural) mechanistic features rather than also on circumstantial/contextual changes occurring in a similar fashion over time.	“Shorter-term fluctuations in the measurements of this feature mask a sustained, longer-term upward trajectory indicative of a possible change in the prevailing conditions or underlying mechanisms involved.”* *This is necessarily abstract in the absence of information on the feature, time-frames and context concerned.
ARIMA (Auto-Regressive Integrated Moving Average)	Time Series	“Assuming current dynamics persist, activity levels are likely to remain within a bounded range over the next three periods, with a non-trivial risk of a sharp deviation thereafter.”	The thematic labelling of this technique is appropriate. The use of both “likelihood” and “risk” to describe equivalent properties of the temporal trend described risks implying the latter involved additional analyses (i.e. other than ARIMA).	The inclusion of the phrase “assuming current dynamics persist” helps ensure the inference implied is interpreted as conditional on ‘all else being equal’ (i.e. ceteris parabus).	“Conditional on the fitted ARIMA dynamics, forecasts of measurable activity levels are likely lie within X%* intervals for three periods, but less likely to remain within these intervals thereafter.” *To better define “a bounded range”.
Bayesian Analysis	Probabilistic Modelling	“Given the new reporting, confidence in hypothesis A has increased substantially, while alternative explanations now carry materially lower probability.”	The thematic labelling of this technique is appropriate. The use of the term “confidence” in this (analytical) setting is problematic given its use to signify ‘precision’ in statistics, and ‘evidentiary strength’ in intelligence analysis.	The (mis)use of the term “confidence” as a synonym for likelihood/probability implies that both the likelihood and the precision of “hypothesis A” has increased; while only the likelihood of alternative hypotheses have declined.	“The a posteriori probability for hypothesis A increased following the availability of this new evidence, with the probabilities of mutually exclusive alternative hypotheses being correspondingly reduced.”

Table 2. (part 2 of 3). An assessment of the potential methodological misrepresentation, and inferential misinterpretation of the “typical analytical insights” Duffield (2026) drafted for next 4 of the 11 “statistical analytical techniques” he proposed intelligence analysts should be competent to apply and interpret; together with alternative descriptions intended to attenuate the risk of misrepresentation or misinterpretation.

“Technique”	“Theme”	“Typical Analytical Insight”	Potential methodological misrepresentation	Potential inferential misinterpretation	Alternative description
ANCOVA (Analysis of Covariance)	Causal Inference	“Once baseline capability and environment are accounted for, the apparent gap between actors narrows significantly, indicating that much of the observed difference reflects starting conditions rather than divergent behaviour.”	The thematic labelling of this technique is inappropriate – ANCOVA is a ‘general linear model’ that can only identify associations between variables (but see below). Such associations can nonetheless support causal inference where they examine: focal relationships between preceding and subsequent variables; and after competently mitigating the risk of confounder and collider bias.	The original “typical analytical insight”, as drafted, presents only limited potential for inferential misinterpretation. The use of the phrase “narrows significantly” implies that the technique routinely provides a statistical measure of the similarity between ‘actor types’ (which it does not) and that this measure achieved a probability considered “significant”.	“The extent of the difference observed between different types of actors is substantively reduced following adjustment for baseline capability and environment, suggesting that much of the difference observed is due to their different starting conditions rather than subsequent developments”* *This is somewhat vague without information on what “differences” between actors were examined.
Trend Plotting	Time Series	“The underlying trajectory shows a sustained upward movement over multiple periods, with short-term volatility masking a longer term structural change.”	The thematic labelling of this technique is appropriate. The use of the phrase “structural change” may exceed the evidence (of ‘underlying mechanism’) this technique can provide – although this will ultimately depend upon what variables/features have been modelled in this analysis.	There is a risk that the phrase “structural change” may encourage solely those inferences that focus on (structural) mechanistic features rather than also on circumstantial/contextual changes occurring in a similar fashion over time.	“Shorter-term fluctuations in the measurements of this feature mask a sustained, longer-term upward trajectory indicative of a possible change in the prevailing conditions or underlying mechanisms involved.”* *This is necessarily abstract in the absence of information on the feature, time-frames and context concerned.
ARIMA (Auto-Regressive Integrated Moving Average)	Time Series	“Assuming current dynamics persist, activity levels are likely to remain within a bounded range over the next three periods, with a non-trivial risk of a sharp deviation thereafter.”	The thematic labelling of this technique is appropriate. The use of both “likelihood” and “risk” to describe equivalent properties of the temporal trend described risks implying the latter involved additional analyses (i.e. other than ARIMA).	The inclusion of the phrase “assuming current dynamics persist” helps ensure the inference implied is interpreted as conditional on ‘all else being equal’ (i.e. ceteris parabus).	“Conditional on the fitted ARIMA dynamics, forecasts of measurable activity levels are likely lie within X%* intervals for three periods, but less likely to remain within these intervals thereafter.” *To better define “a bounded range”.
Bayesian Analysis	Probabilistic Modelling	“Given the new reporting, confidence in hypothesis A has increased substantially, while alternative explanations now carry materially lower probability.”	The thematic labelling of this technique is appropriate. The use of the term “confidence” in this (analytical) setting is problematic given its use to signify ‘precision’ in statistics, and ‘evidentiary strength’ in intelligence analysis.	The (mis)use of the term “confidence” as a synonym for likelihood/probability implies that both the likelihood and the precision of “hypothesis A” has increased; while only the likelihood of alternative hypotheses have declined.	“The a posteriori probability for hypothesis A increased following the availability of this new evidence, with the probabilities of mutually exclusive alternative hypotheses being correspondingly reduced.”

Table 2. (part 3 of 3). An assessment of the potential methodological misrepresentation, and inferential misinterpretation of the “typical analytical insights” Duffield (2026) drafted for final 3 of the 11 “statistical analytical techniques” he proposed intelligence analysts should be competent to apply and interpret; together with alternative descriptions intended to attenuate the risk of misrepresentation or misinterpretation.

“Technique”	“Theme”	“Typical Analytical Insight”	Potential methodological misrepresentation	Potential inferential misinterpretation	Alternative description
Monte Carlo Simulation	Probabilistic Modelling	“Over thousands of simulations, four plausible scenarios emerged, including a sharp deterioration scenario, which occurs when both X and Y occur at a similar time.”	The thematic labelling of this technique is appropriate. Inadequate detail on the number of emerging/evident scenarios (regardless of “plausibility”). Citing “thousands of simulations” (not unusual for this technique) is superfluous and misrepresents the assiduousness of its application.	There is a modest risk of unintended/implied causal inference from “when both X and Y occur” – particularly were (i) “at a similar time” to be taken for ‘just before’; or (ii) no subsidiary analyses to have been performed so as to explore all possible ‘variable-scenario co-occurrences’.	“(Under the assumed input distributions, at least)* four scenarios are evident, one of which involves a sharp deterioration that is associated with the co-occurrence of X and Y” *The original “typical analytical insight” would benefit from adding this disclaimer and clarifying how many scenarios are evident.
Cross-Validation	Cross-Validation	“The model’s predictive performance remains stable across unseen data, indicating that the identified patterns are likely to generalise rather than reflect overfitting.”	The thematic labelling of this technique is appropriate. The only modest risk of misrepresentation lies in the absence of information on the criteria determining the selection of the “unseen data” used to evaluate the “model’s predictive performance”.	The apparent ‘generalisability’ of the ‘predictive’ patterns poses a modest risk of misinterpretation as mechanistic (and hence ‘causal’) were customers to mistake algorithmic/probabilistic ‘prediction’ (a type of estimation, similar in inferential value to an ‘association’) for causally definitive insight.	“The performance of the model across unseen datasets is consistent across folds, suggesting that the patterns identified are generalizable to these datasets.”
Bootstrapping	Bootstrapping	“Across thousands of resampled datasets, the key estimate remains tightly clustered, suggesting the conclusion is robust and not driven by a small number of observations.”	The thematic labelling of this technique is appropriate. Citing “thousands of resampled datasets” (not unusual for this technique) is superfluous and misrepresents the assiduousness of its application. Alternative sources of non-robust clustering (beyond “a small number of observations”) warrant including in such summaries of this technique where relevant.	The fact that bootstrapping offers some reassurance that “key estimate(s)” of smaller sample sizes have been appropriately quantified (always) poses a modest risk that such estimates are mistaken as representative of the population from which the “small number of observations” were drawn – a sample size that nonetheless poses a substantive risk of being unrepresentative.	“Bootstrap resampling yielded a narrow sampling distribution for the estimate – indicating that, despite the small number of observations, the key estimate generated from the sample had substantial statistical precision.”

Table 2. (part 3 of 3). An assessment of the potential methodological misrepresentation, and inferential misinterpretation of the “typical analytical insights” Duffield (2026) drafted for final 3 of the 11 “statistical analytical techniques” he proposed intelligence analysts should be competent to apply and interpret; together with alternative descriptions intended to attenuate the risk of misrepresentation or misinterpretation.

“Technique”	“Theme”	“Typical Analytical Insight”	Potential methodological misrepresentation	Potential inferential misinterpretation	Alternative description
Monte Carlo Simulation	Probabilistic Modelling	“Over thousands of simulations, four plausible scenarios emerged, including a sharp deterioration scenario, which occurs when both X and Y occur at a similar time.”	The thematic labelling of this technique is appropriate. Inadequate detail on the number of emerging/evident scenarios (regardless of “plausibility”). Citing “thousands of simulations” (not unusual for this technique) is superfluous and misrepresents the assiduousness of its application.	There is a modest risk of unintended/implied causal inference from “when both X and Y occur” – particularly were (i) “at a similar time” to be taken for ‘just before’; or (ii) no subsidiary analyses to have been performed so as to explore all possible ‘variable-scenario co-occurrences’.	“(Under the assumed input distributions, at least)* four scenarios are evident, one of which involves a sharp deterioration that is associated with the co-occurrence of X and Y” *The original “typical analytical insight” would benefit from adding this disclaimer and clarifying how many scenarios are evident.
Cross-Validation	Cross-Validation	“The model’s predictive performance remains stable across unseen data, indicating that the identified patterns are likely to generalise rather than reflect overfitting.”	The thematic labelling of this technique is appropriate. The only modest risk of misrepresentation lies in the absence of information on the criteria determining the selection of the “unseen data” used to evaluate the “model’s predictive performance”.	The apparent ‘generalisability’ of the ‘predictive’ patterns poses a modest risk of misinterpretation as mechanistic (and hence ‘causal’) were customers to mistake algorithmic/probabilistic ‘prediction’ (a type of estimation, similar in inferential value to an ‘association’) for causally definitive insight.	“The performance of the model across unseen datasets is consistent across folds, suggesting that the patterns identified are generalizable to these datasets.”
Bootstrapping	Bootstrapping	“Across thousands of resampled datasets, the key estimate remains tightly clustered, suggesting the conclusion is robust and not driven by a small number of observations.”	The thematic labelling of this technique is appropriate. Citing “thousands of resampled datasets” (not unusual for this technique) is superfluous and misrepresents the assiduousness of its application. Alternative sources of non-robust clustering (beyond “a small number of observations”) warrant including in such summaries of this technique where relevant.	The fact that bootstrapping offers some reassurance that “key estimate(s)” of smaller sample sizes have been appropriately quantified (always) poses a modest risk that such estimates are mistaken as representative of the population from which the “small number of observations” were drawn – a sample size that nonetheless poses a substantive risk of being unrepresentative.	“Bootstrap resampling yielded a narrow sampling distribution for the estimate – indicating that, despite the small number of observations, the key estimate generated from the sample had substantial statistical precision.”

5.1. Do These “Typical Analytical Insights” Methodologically Misrepresent the Techniques Involved?

From Table 2 it is clear that almost all of the “typical analytical insights” – as originally drafted by Duffield (2026) – misrepresent the methodological intricacies and conditionalities of each of the techniques concerned, albeit to a varying degree. For the most part the level of misrepresentation may appear relatively trivial, or potentially justifiable on the basis that the less cautious wording used was deemed necessary to simplify and communicate these “insights” to non-specialist audiences (including intelligence analysts or customers yet to be trained in each of the 11 statistical analytical techniques). Yet all too often the drafted “insight” omits or unhelpfully obfuscates inferentially crucial methodological details, such as:

• the intended ‘analytical objective’ of the “typical” example/application used as a basis for drafting each technique’s “insight” (i.e. whether the objective be for descriptive, ‘predictive estimation’, optimisation and/or causal inference purposes) – an issue affecting all of the examples/applications and “insights” drafted for these 11 techniques; and a particular issue for those techniques that can be modelled in different ways to inform more than one analytical objective;
• which covariates were adjusted for/conditioned upon – as for: the “other variables” that were “controll[ed] for” in the “insight” drafted for Linear Regression; and variables relevant to “baseline capability and environment” that were “accounted for” in the “insight” drafted for ANCOVA;
• what other additional/subsidiary/ancillary techniques were involved to generate additional findings that would not have been generated by the principal technique concerned – as for: the “threshold effect” in the “insight” drafted for Logistic Regression; the “natural” separation of “distinct groupings” (and the “material” nature of these groupings’ “risk profiles”) in the “insight” drafted for K-Means Clustering; the “[statistical] significance” of the “narrow[ing]” of differences between “[different groups of] actors” in the “insight” drafted for ANCOVA; the “sharp[ness]” of the “deviation” in the “insight” drafted for ARIMA; and the “structural” nature of the “longer term… change” in the “insight” drafted for Trend Plotting;
• whether any extrapolated estimates of future phenomena/trends might be subject to the assumption of ceteris parabus (all other things being equal/remaining unchanged) – as would be the case for the risk-associated inference of “actor” classification inferred in the “insight” drafted for K-Nearest Neighbours; and
• the meaning of value-laden claims (and, where possible, the quantification of such claims) – as for the “bounded range” and “non-trivial[ity]” of trends in “activity levels” in the “insight” drafted for ARIMA; the “substantially… increased… confidence” and “materially lower probability” in the “insight” drafted for Bayesian Analysis; and the “sharp deterioration” in the “insight” for Monte Carlo Simulation.

Besides these omissions and obfuscations, there was also one instance where the technique had been substantively misrepresented – this being the “causal inference” thematic label applied to the Analysis of Covariance (ANCOVA). While this technique can support models capable of generating (probabilistic) causal inference (as well as models whose analytical objective is ‘predictive estimation’ or optimisation) so can other, predominantly correlational/associational techniques, such as Linear and Logistic Regression – both of which, in this instance, had been thematically labelled methodologically as “regression”, rather than inferentially, as “causal inference” and/or ‘predictive estimation’.

That said, the “causal inference” thematic label applied to ANCOVA (and only thereto), did not appear to have substantively undermined the “typical analytical insight” drafted for this technique. Indeed, its summary of the impact of “account[ing] for…baseline capability and environment[-related covariates]” on the “apparent gap between [groups of] actors” is largely coherent from a methodological and inferential point of view. The “insight” drafted for this technique nonetheless failed to mention the additional/subsidiary/ancillary technique(s) that would have been required to determine whether the “narrow[ing of the]… gap” was “[statistically] significant” – something that ANCOVA alone does not routinely or directly assess.

Taken in the round, these misrepresentations fall substantively short of the more comprehensive, carefully worded and detailed descriptions that might otherwise have ensured that each of the drafted “insights” offered unambiguous yet accessible/non-technical summaries of what each of the 11 techniques were able to provide.

5.2. Do these “typical analytical insights” lead to the inferential misinterpretation of the techniques involved?

As a result of the omissions, obfuscations and misrepresentations summarised in Section 5.1 and Table 2 (above), many of the “typical analytical insights” (as originally drafted) present multiple opportunities for (potential) inferential misinterpretation. These include those: that reflect the paucity of methodological information available to fully understand precisely how each of the techniques (and any additional/subsidiary/ancillary techniques) had been applied; and where the inferences offered/implied by the “insights” (as drafted) go some way beyond what the techniques concerned are able to support:

• Linear Regression – This analytical technique can be used to support causal inference based on bivariate associations evident within observational datasets (in this instance that: “X is a… driver [for Y]”) but only under very specific conditions (these being: temporal-consistency; dataset representativeness; and the availability, and selection, of an appropriate covariate adjustment set; see ANCOVA, below for more details). Even when these conditions hold, this technique is not able to determine definitively whether any such association is “meaningful”, since the specified cause/”driver” (in this instance: “X”) may only be incidentally/indirectly associated with a direct cause of Y (since such an association can also occur through chance, unacknowledged collider bias, or as a result of unadjusted/unmeasured/residual confounding). The “insight” as drafted therefore warrants revision to: temper these explicit inferential claims (and their narrow, and potentially unfounded/unsound, interpretations); or better detail the methodological dependencies upon which these rely (including each of the specific conditions – temporal-consistency, dataset representativeness, and appropriate adjustment set composition – necessary for generating probabilistic causal inference from observational datasets; and any additional techniques applied to assess the “meaningful”-ness of the causal link inferred between “X” and “Y”).
• Logistic Regression – This analytical technique can be used to determine whether the ‘odds’ of a binary outcome (in this instance: the “probability of event A” occurring vs. not occurring) is higher/lower, stronger/weaker or more/less precise in the presence/absence of other “factors”. However, this technique neither provides nor supports inferential assessment as to whether a “threshold effect” is/is not present, or what “factors” might be associated with (or responsible for) such an effect’s ‘inflection point’, unless the model(s) used is(are) designed so as to support such assessments. It is also at risk of inferential misinterpretation were “factors X and Y” to have occurred/crystalised after “event A” happened (i.e. as potentially direct/indirect consequences of “A”); before “event A” (i.e. as potentially direct/indirect causes of “A”); or, indeed, were these “factors” to be ‘mathematically coupled’ to, or indivisible components/features of, “event A”. The apparent relationship between (the presence/absence of) “X” and “Y” and the odds of “event A” will likewise only be consistent with a causal relationship under very specific conditions (these being: temporal-consistency; dataset representativeness; and the availability, and selection, of an appropriate covariate adjustment set; see ANCOVA, below for more details). The “insight” as drafted therefore warrants revision to: temper these inferential claims (and their narrow, and potentially unfounded/unsound, interpretations); or better detail the methodological dependencies upon which these rely (including any additional modelling/analytical techniques applied to assess the: nature of the relationship between “X” and “Y” and “event A”; and presence of a potential “threshold effect”).
• K- Nearest Neighbours – This analytical technique can be used to classify/group entities, events, processes or characteristics thereof with regard to similarities in related features (in this instance: “recent behaviour”). However, it does not necessarily provide or support inferential assessment as to whether any group member so classified necessarily shares the subsequent risk profile of all/most of the other group members (in this instance: “a small subset of previously observed cases”), unless: such inference involved risk-relevant outcomes (in this instance: “outcome B” or causes/determinants thereof) that were components of, mathematically coupled to, or (manifestly/latently, and directly/indirectly) causally associated with, the variables used for classification/grouping; and all necessary and sufficient factors/circumstances required for the “historical… outcome[s]” concerned to remain in place. The “insight” as drafted therefore warrants revision to: temper these inferential claims (and their potentially unfounded/unsound interpretations); or better detail the methodological dependencies upon which these rely (including the inclusion of risk-relevant/related components/correlates/latent features within the classification models; and the temporal stability of any factors/circumstances on which “outcome B” depends).
• K-Means Clustering – This analytical technique can be used to classify/group entities, events, processes or characteristics thereof with regard to similarities in related features (in this instance: “recent behaviour”). However, it does not necessarily provide or support inferential assessment as to: why the groupings are evident or how they arise (in this instance: whether “naturally” vs. artefactually); or the nature/extent of any group-specific meta-features (in this instance: “internally consistent patterns”) or group-related differences in risk profiles (in this instance: whether “material” vs. intangible/insubstantial), unless: such inference involved risk profile-relevant/related features that were components of, mathematically coupled to, or (manifestly/latently, and directly/indirectly) causally associated with, the variables used for classification/grouping; and all necessary and sufficient factors/circumstances required for the “risk profiles” concerned to remain in place. The “insight” as drafted warrants revision to temper these inferential claims (and their potentially unfounded/unsound interpretations); or better detail the methodological dependencies upon which these rely (including the inclusion of: what techniques/measures were used to determine whether the groupings “separate… naturally”, and the “internally consistent patterns” and “materially different risk profiles” described; and the inclusion of risk-relevant/related components/correlates/latent features within the classification models).
• ANOVA (Analysis of Covariance) – As its “thematic classification” suggests, this analytical technique can be used to inform (probabilistic) causal inference (as can other, predominantly associational/correlational analytical techniques, such as Linear and Logistic Regression; see above) but only – as mentioned earlier – under very specific conditions. These are: temporal-consistency (such that: the specified cause precedes its specified consequence; and any covariates controlled/adjusted for/conditioned upon precede both the specified cause and consequence); dataset representativeness (to mitigate the risk of a form of collider bias, known as ‘endogenous selection bias’; Elwert and Winship, 2014); and the availability, and selection, of an appropriate, and appropriately diverse, covariate adjustment set (so as to optimally mitigate the risk of measured/measurable confounding, while avoiding any additional risk of collider bias resulting from inappropriate adjustment for variables that occur after the specified cause and/or consequence; Ellison, 2023). In the “insight” originally drafted for this technique, the risk of inferential misinterpretation is modest, despite the technique being thematically misclassified as (predominantly/solely) “causal inference”. Nonetheless, the allusion to a narrowing of an “apparent gap” between (presumably) different groups of “actors” after “accounting for… baseline capability and environment” does imply that the latter were considered potential sources of confounding that, once “accounted for” (presumably through inclusion of relevant variables in the model’s covariate adjustment set), revealed a much narrower gap between the actors – suggesting that (groups of) different “actors” were more similar in terms of their (more recent) “behaviour” than was “apparent” prior to adjustment. This constitutes causal inference in the sense that the (confounding-adjusted) differences between “actors” was found to be small, and therefore predominantly caused by preceding differences in “baseline capability and environment” (i.e. factors acting as bona fide ‘confounders’) rather than contemporaneous divergence in behaviour. Meanwhile, the use of the phrase “narrows significantly” implies that an additional statistical technique will have been used to assess the statistical significance of the reduction observed following adjustment – an assessment that ANCOVA does not ordinarily or directly provide (unless specifically modelled and configured to support this). For these reasons, the “insight” as drafted warrants revision to better qualify these inferential claims (not least with more detail concerning the nature of the “apparent gap between actors”) so as to facilitate greater understanding of what role “divergent behaviour” might play, whether as a specified consequence of “actor” identity, or as a mediator on the causal path between “actor” identity and a separately specified consequence; and better detail the methodological dependencies upon which these rely (including the inclusion of: what techniques/measures were used to assess how the “gap between actors narrow[ed] significantly” following adjustment for “baseline capability and environment”).
• Trend Plotting – While often mistaken for a purely descriptive, univariable technique, Trend Plotting is essentially a bivariable analysis that helps reveal any sequential variation in a specified target/outcome variable in relation to the changing value of a second ordinal or continuous variable (such as a ranked feature or, more commonly, time). It is capable of elucidating and mapping past/current patterns in this variation and thereby offering a retrospective/historical basis upon which past variation might be better characterised (and – potentially – the mechanisms responsible better understood, and applied to generate ‘foresight’ of possible future trends and the ‘predictive estimation’ of dataset features through extrapolation. In the drafted “insight” provided, the inferential claims appear modest since they simply describe the presence of an historical “sustained… longer term… upward movement” that is otherwise, to some degree, obscured by “short-term volatility” – claims that are based solely on extant empirical information. However, where this “insight” does stretch the inferential capabilities of the technique concerned is in suggesting that such (historical) patterns can “show… [evidence of] structural change”. While the specific example and context to which this “insight” refers might potentially clarify/justify such a claim, the omission of this information from the text of the “insight” implies a level of mechanistic/structural understanding that goes beyond what the technique itself can support. The “insight” as drafted therefore warrants revision to temper these inferential claims (and their potentially unfounded/unsound interpretations); or better detail the contextual/situational and methodological dependencies upon which these rely (including the inclusion of: why the “sustained upward movement” is felt to reflect a longer term “structural change” as opposed, for example, to a regular and sustained series of inputs [of some form or another] that might plausibly have elicited such a trend; and so on).
• ARIMA (Auto-Regressive Integrated Moving Average) – In common with Trend Plotting (see above), this is a bivariable technique that can help reveal any sequential variation in a specified target/outcome variable in relation to the changing value of a second ordinal or continuous variable (such as a ranked feature or, more commonly, time). It is similarly capable of elucidating and mapping past/current patterns in such variation and thereby offering a retrospective/historical basis upon which past variation might be better characterised (and – potentially – the mechanisms responsible, and any possible future trends, speculatively inferred, understood or estimated, respectively). Such future trends are estimated through mathematical/statistical extrapolation (commonly, if unhelpfully, called ‘prediction’), albeit under the assumption of ceteris parabus (all other things being equal/remaining unchanged). Indeed, the drafted “insight” provided for this technique begins with a disclaimer to this effect (“assuming current dynamics persist”) before characterising the estimated future trend in “activity levels… over the next three periods [of time]”. In this regard the inference implied appears both clear and defensible, though the absence of any qualification as to what is meant by: the future trend “remain[ing] within a bounded range” (the meaning of which is entirely predicated on the size/scale of the “range” concerned); or a “non-trivial risk” and a “sharp deviation” – substantively detracts from the import of any inference implied. The “insight” as drafted therefore warrants revision to better clarify and qualify these inferential claims (and their potentially unfounded/unsound interpretations); by offering more detail on any quantifiable measures of the “bounded range”, “trivial risk” and “sharp deviation” to which it refers.
• Bayesian Modelling – This (broad group) of techniques, in which ‘prior’ hypotheses concerning the distributional and correlational properties of datasets are tested against new information/data (as this becomes available), offer an attractive alternative to more commonplace ‘frequentist’ techniques – particularly for those analysts who are keen to test their prior understanding (whether speculative or confident) of the contexts and mechanisms in which, and through which, their analytical objectives/problem sets arise. In the “insight” drafted for this technique, the inference is that “new reporting” has confirmed the hypothesised prior(s) and thereby increased the “[analytical] confidence” therein (while “lower[ing the] probability [or likelihood that]… alternative explanations” [are sound]). Whether the technique (as applied in this instance) supports such inference will depend in no small part on the basis upon which the ‘prior’ was derived, and whether the “new reporting” constituted a contribution that was: independent of whatever empirical/theoretical/speculative evidence led to the analyst’s ‘prior’; and capable of challenging/falsifying/qualifying their initial hypothesis. Provided both of these conditions hold, the “insight” as drafted should not lead to inferential misinterpretation – although the use of the term “confidence” to reflect the finding that the ‘prior’/hypothesis was consistent with “new reporting” is unfortunate given “confidence” is more commonly used (in statistical parlance) with reference to precision, and its use here might therefore prompt misinterpretation. Likewise, the use of “materially” to describe (and thereby substantiate) the “lower probability [of]… alternative explanations” would benefit from more detailed (and, where possible/appropriate, quantitative) qualification, alongside further detail on any additional/subsidiary/ancillary techniques used to assess this. The “insight” as drafted therefore warrants revision to better clarify and qualify these inferential claims (and their potentially unfounded/unsound interpretations); by offering more detail on: how the ‘prior’ hypothesis was developed, and in what sense the “new reporting” might constitute an appropriately rigorous/robust test thereof; and what techniques/measures were used to determine “confidence in hypothesis A”, and the “material[ity]” of the “lower probability” observed for the “alternative explanations”.
• Monte-Carlo Simulation – Though lacking in methodological detail (and notwithstanding the unnecessary reference to “thousands of simulations”, given these are germane to this technique), the drafted “insight” in this instance explicitly invites inference regarding the four “plausible” scenarios supported by the distributional and correlational properties of the (resampled) dataset available. Assuming, once more, that the resampling and algorithmic procedures were appropriately applied, such inference is nonetheless predicated upon: precisely how (and with what criteria) “emerg[ing]… scenarios” were considered “plausible”; why only one of these scenarios was deemed necessary/relevant to describe in any (additional) detail; and how both a “sharp” change and a “deterioration” (as in “sharp deterioration”) were defined, identified and classified as such. The “insight” as drafted therefore warrants revision to better clarify and qualify these inferential claims (and their potentially unfounded/unsound interpretations); by offering more detail on: the methodological procedures employed; all four of the “plausible” scenarios these procedures identified; how the “plausib[ility]” of “emerg[ing]… scenarios” was determined (particularly if any statistical tests/parameters informed their determination); and how both “sharp” and “deterioration” (and the possible converse, be these: absent or modest; and stability or improvement, respectively) were defined and determined (including, as before, detail of any additional/subsidiary/ancillary techniques statistical tests and parameters used to judge such assessments).
• Cross-Validation – This technique’s “insight” – assuming, once more, that the choices/decisions made were appropriate to the dataset, context and analytical objective/problem set concerned – explicitly infers that the original model can be considered appropriate to the dataset examined simply because its predictive performance “remains stable” when tested in subsidiary (hence “unseen”) datasets other than that/those used to ‘train’ the initial model(s)/algorithm(s). While such findings are consistent (and therefore reasonable) evidence that the original model was “generalis[able” and unlikely to have been “overfitted” to the original ‘training’ dataset, such inference substantively depends upon: the complexity of the dataset; and the inherent variability of the distributional and correlation properties of its constituent variables – and whether both the dataset- and data-generating mechanisms are inherently stable (i.e. structurally and statistically conserved, regardless of context – as can be the case with artefacts and contexts governed by tight ‘rules’ or design-related constraints). In such instances, this technique may prove less insightful than the inference implied might suggest – unless, that is, prior knowledge/understanding of either/both of these mechanisms was absent, incomplete, imprecise, inaccurate, unreliable or invalid (which may often be the case in intelligence analysis). The “insight” as drafted therefore warrants revision to better clarify and qualify these inferential claims (and their potentially unfounded/unsound interpretations) by offering (or referring back to) more of the detail on: the dataset(s), dataset variables and context(s) examined; and adding further evidence regarding the “patterns… identified” so as to support further inferential interpretation/speculation thereon.
• Bootstrapping – Setting aside the unnecessary reference to “thousands of resampled datasets” – which (like the “thousands of simulations” within the “insight” drafted for Monte Carlo Simulation; see above) is germane to this technique – the “insight” drafted suggests it did not achieve the principal benefit for which Bootstrapping is most commonly applied – this being to generate more precise (i.e. “[more] tightly clustered”) “key estimate[s]” than would otherwise be possible in datasets containing a relatively “small number of observations” (given the higher risk of chance sampling/measurement imprecision therein). Since, in this instance, the “key estimate remains tightly clustered” (italicised emphasis added), the self-evident inference on this occasion is that the original level of “cluster[ing]” (or precision) observed across the whole of the dataset – given this had a relatively “small number of observations” – does not improve despite the application of bootstrapping. Alternatively, one might assume that the analytical objective behind the use of this technique (on this occasion) was to challenge whether a more “tightly clustered… key estimate” than was initially considered possible/likely might have been a chance phenomenon given the “small number of observations” from which this “key estimate” was derived. Yet bootstrapping is unlikely to offer a robust assessment of the potential for ‘Type 1’ errors of this sort, since “tightly clustered… key estimate[s]” generated initially using the entire dataset are unlikely to prove less “tightly clustered” (i.e. less precise) following bootstrapping simply because, by definition, the scope for imprecision is clearly already limited. The “insight” as drafted therefore warrants revision to better clarify and qualify these inferential claims (and their potentially unfounded/unsound interpretations) by including additional information relevant to the analytical objective the technique was deployed to address.

6. Are Duffield’s 11 Techniques Suitable for Intelligence Analysts with “a Relatively Low Mathematical Baseline”?

It is clear from the preceding Sections of this article that substantial knowledge, care and expertise is required to competently apply (see 1 through 4, above), and succinctly summarise (see 5, above) the 11 “statistical analytical techniques” that Duffield (2026) proposed would “form a strong baseline for… intelligence analysis”. While he himself acknowledged that many intelligence analysts have “a relatively low mathematical baseline”, the scale of the gap between their current statistical competencies and those required to confidently and competently apply each of his 11 proposed technique warrants closer examination – and not least were this to be a relatively narrow gap, and thereby easily addressed through training and/or workplace-based experience and supervision.

Unfortunately, a definitive answer to this question is likely to be elusive, and not simply because different intelligence services/agencies apply different (and often deliberately opaque) criteria when recruiting and developing analysts; and these criteria depend upon the nature of the specialist and generalist qualifications, aptitudes and experience that different intelligence (collection) disciplines and (analytical) specialisms feel the need to apply (MOD, 2023). Some country’s specialist agencies – such as Israel’s ‘Unit 8200’ (which, it is claimed, has been responsible for the rapid proliferation of data science and AI-enabled collection and targeting algorithms during the ongoing conflict in the Middle East; see Yuval, 2024) – go to great lengths to identify recruits with the mathematical, computational and contextual skills, aptitudes and interests deemed necessary for algorithmic innovation (Corera, 2016; Thomas and Kruppa, 2024). However, most entrants into generic intelligence analysis roles do not undergo such targeted selection/recruitment. It is therefore against this lower bar that it is necessary to assess the scale of the gap were these personnel to apply the “core set of [11] statistical analytical techniques” proposed (see Table 1, above).

For want of more accessible example, the current baseline entrance requirements for applicants to intelligence trades of within the UK’s armed forces (see: RN, 2026a; British Army, 2026; and RAF, 2026) are based either on successful completion of a dedicated aptitude test (such as the Royal Navy’s Defence Aptitude Assessment; RN, 2026b) or a Grade 4 (i.e. a ‘standard pass’) or above in GCSE Mathematics. In contrast, entrants into the UK’s armed forces as intelligence officers, or the UK’s civil service intelligence profession, are commonly required to have higher grades in mathematics (either at GCSE or A-Level); while some specialist intelligence disciplines and data-intensive civil service/intelligence agency careers often require entrants to have graduate-level qualifications in mathematics (or substantive evidence/experience of comparable data handling and analysis skills). These higher qualifications aside, it nonetheless seems likely that a good many of those entering intelligence analysis roles in the UK – and therefore those to whom Duffield’s (2026) argument would apply – will only have achieved a ‘standard pass’ in GCSE Mathematics.

Assuming this constitutes the “relatively low mathematical baseline” to which Duffield (2026) refers, the content of the UK’s GCSE Mathematics course should provide a clear indication of the skillsets that those who gain a ‘standard pass’ should possess. This is somewhat complicated by the range of ‘GCSE Mathematics’ courses available. These include: two labelled “GCSE Mathematics” – one at a “Foundation Tier” (offering Grades from 1-5), the other at a “Higher Tier” (offering Grades from 4-9); and four offering a more focussed, or higher Tier, mathematical qualification – these being “GCSE Statistics”, “Level 2 Certificate in Further Mathematics”, “Level 2 EMC (Extended Maths Certificate)”, and “Level 3 FSMQ (Free Standing Mathematics Qualification in Additional Mathematics”). However, since none of these four (more focussed or higher Tier) mathematics qualifications are required for entry into the intelligence branch of the UK’s armed forces, the “baseline” Duffield (2026) describes will be equivalent to a Grade 4 ‘standard pass’ (or above) in either the “Foundation Tier” or “Higher Tier” of GCSE Mathematics.

Both Tiers cover 6 broad topics (core numeracy; basic algebra; ratios; geometry; probability; and statistics) – albeit at a shallower (Foundation Tier) or deeper (Higher Tier) level. The last two of these (probability and statistics) are the most relevant for assessing Duffield’s (2026) premise, and the specific content of each of these (P1-P9; and S1-S6) has been summarised in Table 3a,b, below. Clearly, neither of these topics are taught at a level that would equip those who achieve a ‘standard pass’ to attain the more technical, analytical and inferential, competencies summarised in Table A1.1-A4.2 (see Appendices) without recourse to an extended period of training and/or specialist workplace-based supervision and support. The substantive and opportunity costs associated with such training, supervision and support (and the continuing professional development required to maintain/refresh/update such expertise) are far from insubstantial; and even were the time and resource required to be available, there is clearly a risk that a good number of entrants who currently qualify as competent and proficient intelligence analysts might fail to achieve the mathematical and statistical skills required to take on these additional responsibilities.

Table 3a. Summarised content on “Probability” (hence P1-P9) for the 2026 GCSE Mathematics curriculum, relevant to the Foundation and Higher Tier where appropriate (OxfordAQA, 2026).

Section	Basic foundation content	Additional foundation content	Higher content only
P1	Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees.	[Blank]	[Blank]
P2	Apply ideas of randomness, fairness, and equally likely events to calculate expected outcomes of multiple future experiments.	[Blank]	[Blank]
P3	Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale.	[Blank]	[Blank]
P4	Apply the property that the probabilities of an exhaustive set of outcomes sum to 1.	[Blank]	[Blank]
P5	[Blank]	Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size.	[Blank]
P6	Enumerate sets and combinations of sets systematically, using tables, grids, and Venn diagrams.	[As for Basic, but also] including using tree diagrams.	[Blank]
P7	Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes; and use these to calculate theoretical probabilities.	[Blank]	[Blank]
P8	Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations; and know the underlying assumptions.	[Blank]	[Blank]
P9	[Blank]	[Blank]	Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams.

^aP1 Notes: probabilities should be written as fractions, decimals or percentages. bP8 Notes: including knowing when to add and when to multiply two or more probabilities.

Table 3a. Summarised content on “Probability” (hence P1-P9) for the 2026 GCSE Mathematics curriculum, relevant to the Foundation and Higher Tier where appropriate (OxfordAQA, 2026).

Section	Basic foundation content	Additional foundation content	Higher content only
P1	Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees.	[Blank]	[Blank]
P2	Apply ideas of randomness, fairness, and equally likely events to calculate expected outcomes of multiple future experiments.	[Blank]	[Blank]
P3	Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale.	[Blank]	[Blank]
P4	Apply the property that the probabilities of an exhaustive set of outcomes sum to 1.	[Blank]	[Blank]
P5	[Blank]	Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size.	[Blank]
P6	Enumerate sets and combinations of sets systematically, using tables, grids, and Venn diagrams.	[As for Basic, but also] including using tree diagrams.	[Blank]
P7	Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes; and use these to calculate theoretical probabilities.	[Blank]	[Blank]
P8	Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations; and know the underlying assumptions.	[Blank]	[Blank]
P9	[Blank]	[Blank]	Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams.

^aP1 Notes: probabilities should be written as fractions, decimals or percentages. bP8 Notes: including knowing when to add and when to multiply two or more probabilities.

Table 3b. Summarised content on “Statistics” (hence S1-S6) for the 2026 GCSE Mathematics curriculum, relevant to the Foundation and Higher Tier where appropriate (OxfordAQA, 2026).

Section	Basic foundation content	Additional foundation content	Higher content only
S1	[Blank]	Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling.	[Blank]
S2c	Interpret and construct tables, charts and diagrams, including: frequency tables, bar charts, pie charts and pictograms for categorical data; vertical line charts for ungrouped discrete numerical data; and know their appropriate use.	[As for Basic, but also] including tables and line graphs for time series data.	[Blank]
S3	[Blank]	[Blank]	Construct and interpret diagrams for grouped discrete data and continuous data – i.e. histograms with equal and unequal class intervals, and cumulative frequency graphs; and know their appropriate use.
S4d	Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers).	[Blank]	[As for Basic, but also:] including box plots; and including quartiles and inter-quartile range.
S5	Apply statistics to describe a population.	[Blank]	[Blank]
S6e	Use and interpret scatter graphs of bivariate data; and Recognise correlation.	[As for Basic, but also:] know that it does not indicate causation draw estimated lines of best fit make predictions interpolate and extrapolate apparent trends whilst knowing the dangers of so doing	[Blank]

cS2 Notes: including choosing suitable statistical diagrams. dS4 Notes: students should know and understand the terms: primary data, secondary data, discrete data and continuous data. eS6 Notes: students should know and understand the terms: positive correlation, negative correlation, no correlation, weak correlation and strong correlation.

Table 3b. Summarised content on “Statistics” (hence S1-S6) for the 2026 GCSE Mathematics curriculum, relevant to the Foundation and Higher Tier where appropriate (OxfordAQA, 2026).

Section	Basic foundation content	Additional foundation content	Higher content only
S1	[Blank]	Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling.	[Blank]
S2c	Interpret and construct tables, charts and diagrams, including: frequency tables, bar charts, pie charts and pictograms for categorical data; vertical line charts for ungrouped discrete numerical data; and know their appropriate use.	[As for Basic, but also] including tables and line graphs for time series data.	[Blank]
S3	[Blank]	[Blank]	Construct and interpret diagrams for grouped discrete data and continuous data – i.e. histograms with equal and unequal class intervals, and cumulative frequency graphs; and know their appropriate use.
S4d	Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers).	[Blank]	[As for Basic, but also:] including box plots; and including quartiles and inter-quartile range.
S5	Apply statistics to describe a population.	[Blank]	[Blank]
S6e	Use and interpret scatter graphs of bivariate data; and Recognise correlation.	[As for Basic, but also:] know that it does not indicate causation draw estimated lines of best fit make predictions interpolate and extrapolate apparent trends whilst knowing the dangers of so doing	[Blank]

cS2 Notes: including choosing suitable statistical diagrams. dS4 Notes: students should know and understand the terms: primary data, secondary data, discrete data and continuous data. eS6 Notes: students should know and understand the terms: positive correlation, negative correlation, no correlation, weak correlation and strong correlation.