Statistical Foundation Research Articles

Representable Markov categories and comparison of statistical experiments in categorical probability

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay the foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell–Sherman–Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell–Sherman–Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

Software runtime monitoring with adaptive sampling rate to collect representative samples of execution traces

Monitoring software systems at runtime is key for understanding workloads, debugging, and self-adaptation. It typically involves collecting and storing observable software data, which can be analyzed online or offline. Despite the usefulness of collecting system data, it may significantly impact the system execution by delaying response times and competing with system resources. The typical approach to cope with this is to filter portions of the system to be monitored and to sample data. Although these approaches are a step towards achieving a desired trade-off between the amount of collected information and the impact on the system performance, they focus on collecting data of a particular type or may capture a sample that does not correspond to the actual system behavior. In response, we propose an adaptive runtime monitoring process to dynamically adapt the sampling rate while monitoring software systems. It includes algorithms with statistical foundations to improve the representativeness of collected samples without compromising the system performance. Our evaluation targets five applications of a widely used benchmark. It shows that the error (RMSE) of the samples collected with our approach is 9%–54% lower than the main alternative strategy (sampling rate inversely proportional to the throughput), with 1%–6% higher performance impact.

Developing Young Science and Technology Parks: Recent Findings from Industrial Nations Using the Data-Driven Approach

Science and technology parks (STPs) are curated locations where new technology-based firms (NTBFs) and other SMEs and firms can conglomerate and promote a culture of innovation. Overall, the aim is to construct a sustainable high-value tech entrepreneurship ecosystem, and to this end we present here some recent and novel concepts derived from approaches using a data-driven statistical foundation. This paper considers studies on the organic growth of young start-up science and technology parks by authors who have used big data, econometric analyses, panel data and computer simulations. The results and concepts are derived from industrialized countries, notably Sweden and the UK, and may well be applicable to many regions and emerging economies. The findings are of interest to regional development, technology entrepreneurs considering choosing an STP to inhabit, as well as those in STP central teams, specializing in management and enterprise development, including the sustainable growth of new parks.

Sequential locality of graphs and its hypothesis testing

The adjacency matrix is the most fundamental and intuitive object in graph analysis that is useful not only mathematically but also for visualizing the structures of graphs. Because the appearance of an adjacency matrix is critically affected by the ordering of rows and columns, or vertex ordering, statistical assessment of graphs together with their vertex sequences is important in identifying the characteristic structures of graphs. In this paper, we propose a hypothesis testing framework that assesses how locally vertices are connected to each other along a specified vertex sequence, which provides a statistical foundation for an optimization problem called envelope reduction or minimum linear arrangement. The proposed tests are particularly suitable for moderately small data and formulated based on a combinatorial approach and a block model with intrinsic vertex ordering.

ROLE OF STATISTICS IN ARTIFICIAL INTELLIGENCE

Artificial intelligence (AI) is a rapidly developing field that involves the use of algorithms and machine learning to enable machines to perform humanlike tasks. Statistics is a branch of mathematics that deals with collection, analysis, interpretation, presentation, and organization of data. Statistical methods are widely used in AI to improve performance and accuracy. The purpose of this paper is to examine the role of Statistics in AI. The paper aims to explore the theoretical foundations of AI and Statistics, the statistical methods used in AI, the applications of Statistics in AI, the benefits of integrating Statistics in AI, the challenges and limitations, and the future directions.

Prediction-based uncertainty quantification for exchangeable sequences.

Prediction has a central role in the foundations of Bayesian statistics and is now the main focus in many areas of machine learning, in contrast to the more classical focus on inference. We discuss that, in the basic setting of random sampling-that is, in the Bayesian approach, exchangeability-uncertainty expressed by the posterior distribution and credible intervals can indeed be understood in terms of prediction. The posterior law on the unknown distribution is centred on the predictive distribution and we prove that it is marginally asymptotically Gaussian with variance depending on the predictive updates, i.e. on how the predictive rule incorporates information as new observations become available. This allows to obtain asymptotic credible intervals only based on the predictive rule (without having to specify the model and the prior law), sheds light on frequentist coverage as related to the predictive learning rule, and, we believe, opens a new perspective towards a notion of predictive efficiency that seems to call for further research. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

A Brief Tour of Deep Learning from a Statistical Perspective

We expose the statistical foundations of deep learning with the goal of facilitating conversation between the deep learning and statistics communities. We highlight core themes at the intersection; summarize key neural models, such as feedforward neural networks, sequential neural networks, and neural latent variable models; and link these ideas to their roots in probability and statistics. We also highlight research directions in deep learning where there are opportunities for statistical contributions.

Severe testing of Benford’s law

Benford’s law is often used to support critical decisions related to data quality or the presence of data manipulations or even fraud in large datasets. However, many authors argue that conventional statistical tests will reject the null of data “Benford-ness” if applied in samples of the typical size in this kind of applications, even in the presence of tiny and practically unimportant deviations from Benford’s law. Therefore, they suggest using alternative criteria that, however, lack solid statistical foundations. This paper contributes to the debate on the “large n” (or “excess power”) problem in the context of Benford’s law testing. This issue is discussed in relation with the notion of severity testing for goodness-of-fit tests, with a specific focus on tests for conformity with Benford’s law. To do so, we also derive the asymptotic distribution of the mean absolute deviation (MAD) statistic as well as an asymptotic standard normal test. Finally, the severity testing principle is applied to six controversial large datasets to assess their “Benford-ness”.

Granular approximations: A novel statistical learning approach for handling data inconsistency with respect to a fuzzy relation

Inconsistency in classification and regression problems occurs when instances that relate in a certain way on the condition attributes, do not follow the same relation on the decision attribute. It typically appears as a result of perturbation in data caused by incomplete knowledge (missing attributes) or by random effects that occur during data generation (instability in the assessment of decision attribute values). Inconsistencies with respect to a crisp preorder relation (expressing either dominance or indiscernibility between instances) can be handled with set-theoretic approaches like rough sets and by using statistical/machine learning approaches that involve optimization methods. In particular, the Kotłowski-Słowiński (KS) approach relabels the objects from a dataset such that inconsistencies are removed, and such that the new class labels are as close as possible to the original ones in terms of a given loss function. In this paper, we generalize the KS approach to handle inconsistency determined by a fuzzy preorder relation rather than a crisp one. The method produces a consistent fuzzy relabeling of the instances and may be used as a preprocessing tool with algorithms for binary classification and regression. As the obtained fuzzy sets can be represented as unions of meaningful simple fuzzy sets or granules, we call them granular approximations. We provide statistical foundations for our method, develop appropriate optimization procedures, provide didactic examples, and prove several important properties.

Analysis on the Teaching Reform Countermeasures of the Course "Basic Statistics" under the Concept of Curriculum Ideology and Politics

From the perspective of "curriculum ideological and political" concept, the teaching reform of "Statistics Foundation" is not only related to the development of China's future market economy, but also related to the talent cultivation pattern of the future economic society. However, in the process of the teaching reform of the course "Basic Statistics", teachers should always be clear that the teaching reform under the concept of "curriculum ideological and political" is never about "teaching methodology" and "teaching practice strategy", but should promote the development of students' ideological and political awareness with ideological concepts. Based on this, this paper will briefly describe the concept of "curriculum ideological and political", and on this basis, put forward the objectives and countermeasures of the teaching reform of "Statistics Basis" under the concept of curriculum ideological and political, so as to promote the better development of the teaching reform of "Statistics Basis".

Multiple object tracking with appearance feature prediction and similarity fusion

Object tracking is a crucial research area within the field of intelligent transportation, providing a vital foundation for anomalous behavior analysis and traffic statistics. Although pedestrian detectors have shown impressive results, leading to the advancement of detection-based tracking methods, target association in complex scenarios remains a difficult and less efficient task due to the lack of feature robustness in the presence of partial occlusions. In the proposed tracking method, we extract convolutional features on each entire object and its local blocks, segmented by the superpixel algorithm. Aiming to emphasize the global and local information respectively, the global features for each entire object are extracted from the last layer of the backbone network, while local features are derived from a specific intermediate layer of the backbone network. The association between tracked targets and detected pedestrian candidates relies on fused similarity degrees. Furthermore, we use the transformer’s self-attention mechanism to predict features for the current frame based on the information within past frames, aiming to eliminate the effects of target appearance variations. Additionally, we remove redundant background pixels in the detected rectangles of pedestrian candidates by using a background modeling algorithm. Experimental results demonstrate that the tracker proposed in this paper outperforms other trackers across five publicly available datasets, indicating its effectiveness and potential for further development.

Nonrandomized Techniques for Sensitive Surveys: Comparative Analyses

The article is devoted to the description and analysis of the «crosswise» and «triangular» models, pioneered in 2008 by Hong Kong statisticians Yu, Tian and Tang and belonging to the class of non-randomized survey techniques (NRRT), specifically designed to control the effects of social desirability and stimulate self-disclosure of respondents in sensitive surveys. Based on the results of foreign studies, the author made an attempt to evaluate the possibilities of these models for obtaining sincere answers from the respondents. The paper describes the design features, question-answer logic and statistical foundations of both models under study. Methods for calculating a probabilistic estimate of the prevalence of the studied sensitive behavior are presented. The results of empirical tests are presented, which make it possible to judge the validity of the two techniques. The advantages of the crosswise and triangular models compared to the Warner RRT technique and the self-report method are shown, consisting in high validity, good performance by both respondents and intervie-wers, as well as methodological versatility. The most important shortcomings and limitations of survey techniques related to the respondents' non-compliance with the prescribed instructions and the subjective preferences of the interviewees in relation to certain response options are analyzed. The mechanism of the appearance of false-positive assessments that negatively affect the validity of the final data is revealed. Possible solutions to this problem are proposed. As a result of a comparative analysis of the two studied models, the author comes to the conclusion that the advantage in choosing between these two indirect techniques in terms of practical application remains with the crosswise model due to the symmetry of its question-answer design and more effective control of social desirability effects.

СТАТИСТИЧНЕ ПІДҐРУНТЯ ФОРМУВАННЯ БІЗНЕС-МОДЕЛІ ПІДПРИЄМСТВА В УМОВАХ ЦИФРОВОЇ ТРАНСФОРМАЦІЇ

This article is devoted to the problem of forming the right array of information for the formation of an effective business model of the enterprise. The authors stated that in the conditions of digital transformation, statistical information is becoming more and more freely accessible, which, on the one hand, is positive, as it allows comprehensive research of any economic processes; and on the other hand, this leads to overloading of the system, the impossibility of distinguishing the main and reliable, and as a result – those parameters that have the highest degree of influence and effectiveness on the enterprise are not always taken into account. The processes of digitization of the economy have greatly facilitated the processes of access to various types of information. It became available to use statistical information in the implementation of scientific activities, development of strategies and formation of business models, management decisions, etc. The fact that digital transformation has a positive effect on the acceleration of all digital processes and allows for a significant increase in work productivity is undeniable. However, due to the large amount of statistical information, it is often quite difficult to assess its relevance and truthfulness. When forming a business model for business development, the timeliness of its implementation and the possibility of adjustment are important. Accordingly, the availability of statistical information and its correct and effective use allows to speed up such processes and remain on the market with the appropriate level of competitiveness. In the process of research, the main criteria were determined, which, according to the authors, should have a statistical basis when forming a business model, possible errors and problems arising during the collection, processing and use of statistical information were outlined, the impact of digital transformation on the effectiveness of building a business model of domestic enterprises was clarified enterprises. The authors of the article summarized the problems of forming a statistical foundation when developing a business model of an enterprise and proposed the main criteria that require digital support.

A new database on Green GDP; 1970-2019: a framework for assessing the green economy

Research background: Numerous modern indicators are attempting to integrate better economic, political, social, and environmental ambitions to uncover potential synergy, trade-offs, and future views that center around the notion of a so-called green economy. As long as the various indicators are not bounded in one comprehensive measurement, utilizing knowledge of relevant information and statistics that are crucial for monitoring the progress will not give us answers on the progress towards green growth either. Without an adequate measurement framework and robust statistics, the evaluation of the green economy is open to subjective reasoning. Purpose of the article: This paper aims to offer a strong standpoint for green topics by exploring the concept of Green GDP. The paper introduces a new, updated database on Green GDP for the set of 160 countries from 1970?2019. Methods: This database is distinctive due to its balanced coverage of two components of the green economy: quantitative feature (standard methodological algorithm) and qualitative feature (opportunity costs) within a common Green GDP accounting framework. Findings & value added: Standardizing new methodologies and procedures for estimating environmental costs with a statistical foundation provides added value, which we hope will support the creation of reliable accounting and valuation systems for the green economy on a developing "green platform."

The Historical Statistics of the Altai Information System

In the era of the digital turn, it is becoming relevant to create information resources that provide researchers with not only background information about historical sources but also reliable historical data. At the all-Russian level, such resources come from library centres (National Electronic Library, Presidential Library), archival authorities (Central Fund Catalogue), and public organisations (Russian Historical Society, Russian Geographical Society). For some regions, this task remains new and requires modern approaches and solutions. The article provides a description of the information system for a set of statistical materials on the history of Altai in the nineteenth – the first half of the twentieth centuries kept in central and regional libraries, archives, digitised publications, and collections with the possibility of versatile search and analysis of historical data. On the one hand, the chronological boundaries of the materials included in the database depend on the formation of the foundations of regular statistics in the mid-nineteenth century, and, on the other hand, on the establishment of Altai Krai within its present-day boundaries in 1937. The territorial framework of the study covers the borders of Altai as a historical region, which was included in the period under review in such administrative-territorial formations as Tomsk and Altai provinces and Siberian and West Siberian regions. The study employs a systematic approach, examining various types of statistical data as elements of a single set of sources on the history of Altai in the nineteenth – first half of the twentieth centuries. In its IT aspect, the study relies on database technology, both a tool and a result of the study. The Historical Statistics of Altai information system was created under the control of MySQL and consists of directories and four main modules: storage, sources, tags, and documents. The authors examine database architecture, logical structure, and data characteristics of the modules. The information system on the historical statistics of Altai will make it possible to solve some of the heuristic tasks related to the search and use of archival, museum, and library funds, including familiarisation with historical sources and their preliminary analysis in remote access mode. As a result, it will significantly expand research opportunities.

The conception of the digital platform of independent assesment of the future teachers

Introduction. Modern processes of digitalization of education put forward new requirements for the procedures for evaluating the results of research results of research results of teachers. Of particular relevance are approaches to the design of digital research tools, including electronic resources that allow consolidating the consumption and evaluation of the educational result by experts with the possibility of implementing an integrative and differentiated evaluation procedure. Materials and Methods. Methods of analysis, systematization and generalization of scientific literature on problematic studies were used. The purpose of the article is to analyze and substantiate the conceptual foundations for creating a digital platform for an independent assessment of the level of achievement of research results by future teachers. Results. The article analyzes approaches to the protection of electronic resources in the fields of education, substantiates the advantages and functionality of the phenomenon of electronic assessment. The conceptual foundations for creating digital platforms are the methodological unity of the platform and ecosystem approach, extended methodological assessments of the foundations for creating an independent educational result system, including systemic, activity-based, criteria-based, competency-based, technological, level-based approaches, objectivity, objectivity, reliability and openness of assessment procedures. The digital platform for independent assessment of the level of achievement of the educational result gives its idea based on the evaluation of the effectiveness of the study of results, the effectiveness of data and their use on the basis of broad procedures and algorithms for assessing the educational result of the observation of teachers, the modularity of the organization of procedures for assessing the educational result, non-linear functionality, partisipatory analytics and evaluation of results , popular results at the lowest cost of resources. The digital platform for independent assessment of the level of achievement of the educational result performs an analytical, predictive, evaluation, information and aggregation function. Discussion and Conclusions. As part of the study of the conceptual and practice-oriented statistical foundations for independent evaluation of the results of teacher research, promising areas for long-term research have been identified: – adding a digital platform for independent evaluation of the results of teachers' observation in the system of teachers' professional growth, accompanying young professionals in the life cycle of the profession; – improvement of the university accreditation system based on the use of a digital platform; – determination of approaches to the combination of emotional, psychological comfort and personality verification processes in the procedures for implementing the evaluation of research results.

On the consistency and asymptotic normality of multiparameter persistent Betti numbers

The persistent Betti numbers are used in topological data analysis (TDA) to infer the scales at which topological features appear and disappear in the filtration of a topological space. Understanding the statistical foundations of these descriptors, and their corresponding barcodes, is thus an important problem that has received a significant amount of attention. There are, however, many situations for which it is natural to simultaneously consider multiple filtration parameters, e.g. when a point cloud comes equipped with additional measurements taken at the locations of the data. Multiparameter persistent homology (MPH) was introduced to accommodate such multifiltrations, and it has become one of the most active areas of research within TDA, with exciting progress on multiple fronts. The present work offers a first step towards a rigorous statistical foundation of MPH. Notably, we establish the strong consistency and asymptotic normality of the multiparameter persistent Betti numbers in growing domains. Our asymptotic results are established for a general framework encompassing both the marked Čech bifiltration, as well as the multicover bifiltration constructed on the null model of an independently marked Poisson point process. In a simulation study, we explain how the asymptotic normality can be used to derive tests for the goodness of fit. The statistical power of such tests is illustrated through different alternatives exhibiting more clustering, or more repulsion than the null model.

Bayesianism from a philosophical perspective and its application to medicine.

Bayesian philosophy and Bayesian statistics have diverged in recent years, because Bayesian philosophers have become more interested in philosophical problems other than the foundations of statistics and Bayesian statisticians have become less concerned with philosophical foundations. One way in which this divergence manifests itself is through the use of direct inference principles: Bayesian philosophers routinely advocate principles that require calibration of degrees of belief to available non-epistemic probabilities, while Bayesian statisticians rarely invoke such principles. As I explain, however, the standard Bayesian framework cannot coherently employ direct inference principles. Direct inference requires a shift towards a non-standard Bayesian framework, which further increases the gap between Bayesian philosophy and Bayesian statistics. This divergence does not preclude the application of Bayesian philosophical methods to real-world problems. Data consolidation is a key challenge for present-day systems medicine and other systems sciences. I show that data consolidation requires direct inference and that the non-standard Bayesian methods outlined here are well suited to this task.

A statistical foundation for derived attention

According to the theory of derived attention, organisms attend to cues with strong associations. Prior work has shown that – combined with a Rescorla–Wagner style learning mechanism – derived attention explains phenomena such as learned predictiveness, inattention to blocked cues, and value-based salience. We introduce a Bayesian derived attention model that explains a wider array of results than previous models and gives further insight into the principle of derived attention. Our approach combines Bayesian linear regression with the assumption that the associations of any cue with various outcomes share the same prior variance, which can be thought of as the inherent importance of that cue. The new model simultaneously estimates cue–outcome associations and prior variance through approximate Bayesian learning. A significant cue will develop large associations, leading the model to estimate a high prior variance and hence develop larger associations from that cue to novel outcomes. This provides a normative, statistical explanation for derived attention. Through simulation, we show that this Bayesian derived attention model not only explains the same phenomena as previous versions, but also retrospective revaluation. It also makes a novel prediction: inattention after backward blocking. We hope that further development of the Bayesian derived attention model will shed light on the complex relationship between uncertainty and predictiveness effects on attention.

Toward a statistical foundation for brain signatures of behavioral outcome

AbstractBackgroundThe “brain signature of cognition” concept has garnered interest as a data‐driven, exploratory approach to better understand key brain regions involved in specific cognitive functions, with the potential to maximally characterize brain substrates of clinical outcomes. However, to be a robust brain phenotype, the signature approach requires a statistical foundation showing that model performance replicates across a variety of cohorts. Here, we outline a procedure that provides this foundation for a signature models of episodic memory and extend this to a measure of functional everyday memory.MethodUniversity of California, Davis (UCD) and ADNI provided imaging and memory data. For cognitive and ECog memory, we derived regional brain gray matter (GM) cortical thickness (CT) measures, testing for replicability (Fig. 1). Signature model generation used two steps in each cohort: 1) Randomly select 40 discovery subsets of size N = 400. In each subset, use voxelwise regression to compute the CT signature regions for outcome at three t‐values of association. 2) Compile frequency maps of region selection across all 40 discovery sets and designate regions with selection frequency >70% as “consensus” signature masks for each cohort. Model validation used regressions of outcomes on consensus masks: 1) Compare adjusted R2 fits of both consensus signature models in 40 discovery sets in each cohort (thus, symmetrically compare same and oppositely generated models). 2) In each full cohort, compare signature model fits with competing models.ResultSpatial replications produced strongly convergent consensus signature regions derived from UCD and ADNI (Fig. 2). Consensus model fits were highly correlated in 40 random subsets of each cohort (Fig. 3 top) indicating high replicability, with tight (∼80%) ratios of within/outside cohort model fits (Fig. 3 bottom), indicating low bias. In comparisons over each full cohort, signature models outperformed other models with one exception (Fig. 4).ConclusionMultiple random model generations, followed by consensus selection of regional brain substrates, produced signature models that both consistently replicated model fits to memory and outperformed other commonly used measures. Results support consensus signature models as robust biomarkers of cognition and everyday function across imaging cohorts with differing demographic composition (see Table).