Statistical Foundation Research Articles

Enhancing Statistical Infrastructure to Improve Economic Census Efficiency

With the continuous development of the economy and societal progress, the economic census, as an important aspect of national statistical work, is directly influenced by the quality of grassroots infrastructure. This paper thoroughly discusses the importance of strengthening the statistical foundation to improve the efficiency of economic census work, analyzes the existing issues in current infrastructure and census processes, and proposes corresponding solutions. By enhancing the professional training of grassroots statisticians, updating data collection technologies, and optimizing workflows, the aim is to significantly improve the accuracy and efficiency of the economic census, providing strong support for the healthy development of the national economy and informed decision-making.

Predicting NEPSE Index: An ARIMA-Based Model

Purpose: This research aims to employ the Auto Regressive Integrated Moving Average (ARIMA) approach to forecast the Nepal Stock Exchange (NEPSE) index.Methods: Daily univariate time series data were taken from the NEPSE website and other sources for 27 years for a total 6143 daily time series data starting in 1997. The presence of unit roots was identified through an Augmented Dickey-Fuller (ADF) test, which ensures stationarity in data. Thereafter, estimation and evaluation of AR (autoregressive), MA (moving average), and ARIMA models were carried out.Results: The study reveals that the ARIMA (2,1,1) model is well fitted in predicting the NEPSE index, indicating its ability to capture temporal dependence and trends that exist within the data.Conclusion: It concludes the temporal dynamics of series highlighting both the short-term impacts of past shocks and longer-term adjustment towards equilibrium. The research work supports the efficacy of model in capturing and predicting the behaviour of NEPSE index, thereby adding in informed decision making and future projections based on proposed statistical foundations.

A mathematical primer to classical deep learning

This manuscript synthesizes the statistical foundations of classical deep learning by integrating insights from eight seminal works. It covers matrix calculus, neuron layers, weight and bias indexing, cost functions, differentiation of neuron operations, activation functions, bias functions, gradient descent, and backpropagation algorithms. The synthesis aims to provide a comprehensive understanding of the mathematical and statistical principles underpinning deep learning models, facilitating their application and further development in various domains.

On the Solute-Induced Structure-Making/Breaking Phenomena: Myths, Verities, and Misuses in Solvation Thermodynamics

We review the statistical mechanic foundations of the fundamental structure-making/breaking functions, leading to the rigorous description of the solute-induced perturbation of the solvent environment for the understanding of the solvation process of any species regardless of the type and nature of the solute–solvent interactions. Then, we highlight how these functions are linked to unambiguous thermodynamic responses resulting from changes in state conditions, composition, and solute–solvent intermolecular interaction asymmetries. Finally, we identify and illustrate the pitfalls behind the use of surrogate approaches to structure-making/breaking markers, including those based on Jones–Dole’s B-coefficient and Hepler’s isobaric-thermal expansivity, while highlighting their ambiguities and lack of consistency and the sources of misinterpretations.

Examining Motivational Attitudes Toward Statistics and Their Relationship to Performance in Life Science Students

A strong foundation of statistics is essential for undergraduates pursuing life science careers, but this foundation is frequently undermined by negative student attitudes toward statistics. This study explored life science students’ motivational attitudes toward statistics, and their relationship to performance, using expectancy-value theory as a guiding framework. According to expectancy-value theory, task-values—interest in a task (intrinsic value), importance of doing well on a task (attainment value), perceptions of the usefulness of a task (utility value), and negative aspects of engaging in a task (cost)—impact achievement outcomes. However, task-values may be better represented by differentiating each into more specific underlying dimensions, or facets. Using 360 undergraduate life science students enrolled in biostatistics courses across two institutions, this study assessed the fit of a task-value facets model for statistics and examined which task-value facets relate to performance on a statistics assessment. Results show that life science students distinguish among facets of attainment value (importance of achievement, personal importance), utility value (school, daily life, social, career/job), and cost (effort, emotional, opportunity) for statistics. Students’ perceptions of the emotional cost of statistics and the importance of achievement in statistics related to their statistics performance. Implications for teaching and research are discussed. Supplementary materials for this article are available online.

Science of science: A multidisciplinary field studying science

Science and knowledge are studied by researchers across many disciplines, examining how they are developed, what their current boundaries are and how we can advance them. By integrating evidence across disparate disciplines, the holistic field of science of science can address these foundational questions. This field illustrates how science is shaped by many interconnected factors: the cognitive processes of scientists, the historical evolution of science, economic incentives, institutional influences, computational approaches, statistical, mathematical and instrumental foundations of scientific inference, scientometric measures, philosophical and ethical dimensions of scientific concepts, among other influences. Achieving a comprehensive overview of a multifaceted field like the science of science requires pulling together evidence from the many sub-fields studying science across the natural and social sciences and humanities. This enables developing an interdisciplinary perspective of scientific practice, a more holistic understanding of scientific processes and outcomes, and more nuanced perspectives to how scientific research is conducted, influenced and evolves. It enables leveraging the strengths of various disciplines to create a holistic view of the foundations of science. Different researchers study science from their own disciplinary perspective and use their own methods, and there is a large divide between quantitative and qualitative researchers as they commonly do not read or cite research using other methodological approaches. A broader, synthesizing paper employing a qualitative approach can however help provide a bridge between disciplines by pulling together aspects of science (economic, scientometric, psychological, philosophical etc.). Such an approach enables identifying, across the range of fields, the powerful role of our scientific methods and instruments in shaping most aspects of our knowledge and science, whereas economic, social and historical influences help shape what knowledge we pursue. A unifying theory is then outlined for science of science – the new-methods-drive-science theory.

Statistics as a Social Activity: Attitudes toward Amalgamating Evidence.

Amalgamation of evidence in statistics is conducted in several ways. Within a study, multiple observations are combined by averaging, or as factors in a likelihood or prediction algorithm. In multilevel modeling or Bayesian analysis, population or prior information is combined with data using the weighted averaging derived from probability modeling. In a scientific research project, inferences from data analysis are interpreted in light of mechanistic models and substantive theories. Within a scholarly or applied research community, data and conclusions from separate laboratories are amalgamated through a series of steps, including peer review, meta-analysis, review articles, and replication studies. These issues have been discussed for many years in the philosophy of science and statistics, gaining attention in recent decades first with the renewed popularity of Bayesian inference and then with concerns about the replication crisis in science. In this article, we review the amalgamation of statistical evidence from different perspectives, connecting the foundations of statistics to the social processes of validation, criticism, and consensus building.

From Wald to Schnorr: von Mises’ definition of randomness in the aftermath of Ville’s Theorem

The first formal definition of randomness, seen as a property of sequences of events or experimental outcomes, dates back to Richard von Mises’ work in the foundations of probability and statistics. The randomness notion introduced by von Mises is nowadays widely regarded as being too weak. This is, to a large extent, due to the work of Jean Ville, which is often described as having dealt the death blow to von Mises’ approach, and which was integral to the development of algorithmic randomness—the now-standard theory of randomness for elements of a probability space. The main goal of this article is to trace the history and provide an in-depth appraisal of two lesser-known, yet historically and methodologically notable proposals for how to modify von Mises’ definition so as to avoid Ville’s objection. The first proposal is due to Abraham Wald, while the second one is due to Claus-Peter Schnorr. We show that, once made precise in a natural way using computability theory, Wald’s proposal constitutes a much more radical departure from von Mises’ framework than intended. Schnorr’s proposal, on the other hand, does provide a partial vindication of von Mises’ approach: it demonstrates that it is possible to obtain a satisfactory randomness notion—indeed, a canonical algorithmic randomness notion—by characterizing randomness in terms of the invariance of limiting relative frequencies. More generally, we argue that Schnorr’s proposal, together with a number of little-known related results, reveals that there is more continuity than typically acknowledged between von Mises’ approach and algorithmic randomness. Even though von Mises’ exclusive focus on limiting relative frequencies did not survive the passage to the theory of algorithmic randomness, another crucial aspect of his conception of randomness did endure; namely, the idea that randomness amounts to a certain type of stability or invariance under an appropriate class of transformations.

Unveiling Malicious Network Flows Using Benford’s Law

The increasing proliferation of cyber-attacks threatening the security of computer networks has driven the development of more effective methods for identifying malicious network flows. The inclusion of statistical laws, such as Benford’s Law, and distance functions, applied to the first digits of network flow metadata, such as IP addresses or packet sizes, facilitates the detection of abnormal patterns in the digits. These techniques also allow for quantifying discrepancies between expected and suspicious flows, significantly enhancing the accuracy and speed of threat detection. This paper introduces a novel method for identifying and analyzing anomalies within computer networks. It integrates Benford’s Law into the analysis process and incorporates a range of distance functions, namely the Mean Absolute Deviation (MAD), the Kolmogorov–Smirnov test (KS), and the Kullback–Leibler divergence (KL), which serve as dispersion measures for quantifying the extent of anomalies detected in network flows. Benford’s Law is recognized for its effectiveness in identifying anomalous patterns, especially in detecting irregularities in the first digit of the data. In addition, Bayes’ Theorem was implemented in conjunction with the distance functions to enhance the detection of malicious traffic flows. Bayes’ Theorem provides a probabilistic perspective on whether a traffic flow is malicious or benign. This approach is characterized by its flexibility in incorporating new evidence, allowing the model to adapt to emerging malicious behavior patterns as they arise. Meanwhile, the distance functions offer a quantitative assessment, measuring specific differences between traffic flows, such as frequency, packet size, time between packets, and other relevant metadata. Integrating these techniques has increased the model’s sensitivity in detecting malicious flows, reducing the number of false positives and negatives, and enhancing the resolution and effectiveness of traffic analysis. Furthermore, these techniques expedite decisions regarding the nature of traffic flows based on a solid statistical foundation and provide a better understanding of the characteristics that define these flows, contributing to the comprehension of attack vectors and aiding in preventing future intrusions. The effectiveness and applicability of this joint method have been demonstrated through experiments with the CICIDS2017 public dataset, which was explicitly designed to simulate real scenarios and provide valuable information to security professionals when analyzing computer networks. The proposed methodology opens up new perspectives in investigating and detecting anomalies and intrusions in computer networks, which are often attributed to cyber-attacks. This development culminates in creating a promising model that stands out for its effectiveness and speed, accurately identifying possible intrusions with an F1 of nearly 80%, a recall of 99.42%, and an accuracy of 65.84%.

Statistics of Periodicals in the Baltic States: Data Sources and Collections

Publishing is a significant part of the cultural, creative, and economic sectors. Its research, assessment, and forecasting require grounded, reliable, accurate, consistent, and comparable statistical data. Considering the lack of research in periodicals statistics and the relevance of publishing statistics, as well as the fact that in the Baltic countries, publishing statistics data are collected by institutions at the same level, the problem arises whether the national libraries’ applied foundational recommendations and legal documents, as well as data collection methodology, can ensure data validity, reliability, comprehensiveness, and comparability. This article aims to examine and compare the data collection practices of periodical statistics in the Baltic States. The research object includes the legal foundation of publishing statistics in Lithuania, Latvia, and Estonia, as well as the 2022 publishing statistics resources and official statistics data collections. UNESCO recommendations and International Organization for Standardization standards can be considered guidelines for such data collection and accounting. The legal foundation of publishing statistics consists of legal deposit laws, which must ensure the sources of statistical data. Even though publishing statistics data are collected by national libraries and the source of statistical data in all countries is legal deposits, the statistical data collections are not identical. Countries choose which data to collect, what criteria to apply, and in what form to present them. It is important to emphasize that data on the publishing industry are not presented in statistical collections, although their collection guidelines and presentation importance are highlighted in international recommendations and normative documents. Statistical data on electronic periodicals are provided only by Estonia. National libraries in the Baltic States are official statistics compilers, so summarized publishing statistics data are provided to national statistics institutions, opening new technological possibilities for data analysis and integration of new data. The collections of statistical data on newspapers and magazines can only be compared according to a few main criteria, as countries have chosen different statistical data presentation features, the main ones being the varying categorization and periodicity characteristics of newspapers and magazines.

Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the Rényi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation.

A regime switch error correction model to project sea level rise

Climate scientists employ various techniques to study the sea level rise (SLR), one of which is semi-empirical approach where the historical relationship between the SLR and global temperature is extracted from the data and parameterized for future SLR projections. It has been documented that semi-empirical models tend to have large variations in the projections depending on the data and methodologies. This study examines the statistical properties of the data used to construct the semi-empirical models and propose a new specification as a regime switch error correction model. We show that the proposed model has sound statistical foundation and good performance. The out-of-sample model projection of cumulative SLR from 2001–2020 is within 10% of the actual SLR. The model projects that in 21st century, the average and the 5%-95% range (in parenthesis) cumulative sea level rise will be 0.28m (0.20–0.36m), 0.41m (0.33–0.48m), or 0.68m (0.60–0.76m), respectively, under the SSP1-2.6/2-4.5/5-8.5 scenarios. These projections are aligned with IPCC AR5 while lower than IPCC AR6. They are also within the range of the projections in recent studies.

Bibliometric Analysis and Visualization of Scientific Literature on Heart Disease Classification Using a Logistic Regression Model.

With the advancement in artificial intelligence, the use of machine learning algorithms for clinical prediction has increased tremendously. Logistic regression is one of the powerful machine learning algorithms that can be used to predict the probability of a variable. Logistic regression is very popular among medical researchers owing to its simplicity, interpretability, and solid statistical foundation. This study aims to investigate the research productivity of heart disease classification using a logistic regression model to analyze the current patterns and potential future trends through bibliometric analysis. Additionally, it aims to highlight the impact and quality of research in the area, identify prominent research groups,the countries actively contributing to the field, which will help the researchers andhealthcare professionals to pinpoint research gaps, influential authors, and make informed decisions and invest resources accordingly. The data is collected from a database of Scopus spanning from 2019 to 2023. We have used two bibliometric software, Biblioshiny(Aria and Cuccurullo, 2017) and VOSviewer (Centre for Science and Technology Studies (CWTS), Leiden University,the Netherlands), to analyze the bibliographic data regarding the citation count, contribution of authors, publication count, the contribution of institutions, etc.There are 2331 documents under study which were fed into both software to analyze the data. With 700 documents, China topped the list of most productive countries indicating the vast contribution of the country followed by India and the United States. Contributions of the Harvard Medical School, Boston, MA, United States are found to be the greatest with six papers. The most productive author is Wang Y with 73 documents. Analysis of trending topics reveals that the field progressing towards using support vector machines (SVM), k-nearest neighbours (KNN), and naïveBayes algorithms. The article has only considered data from Scopus excluding literature indexed in other databases which limits the potential coverage of the data. Also, the work focuses on recent developments excluding older literature from 2019 which could be a limitation. Furthermore, since the study is a bibliometric analysis targeting the use of logistic regression for heart disease prediction, powerfultechniques such as SVM, decision trees, random forests, neural networksand deep learning have not been included, which could be another limitation.

Advancing Solar Energetic Particle Event Prediction through Survival Analysis and Cloud Computing. I. Kaplan–Meier Estimation and Cox Proportional Hazards Modeling

Solar energetic particles (SEPs) pose significant challenges to technology, astronaut health, and space missions. This initial paper in our two-part series undertakes a comprehensive analysis of the time to detection for SEPs, applying advanced statistical techniques and cloud-computing resources to deepen our understanding of SEP event probabilities over time. We employ a range of models encompassing nonparametric, semiparametric, and parametric approaches, such as the Kaplan–Meier estimator and Cox Proportional Hazards models. These are complemented by various distribution models—including exponential, Weibull, lognormal, and log-logistic distributions—to effectively tackle the challenges associated with “censored data,” a common issue in survival analysis. Employing Amazon Web Services and Python’s “lifelines” and “scikit-survival” libraries, we efficiently preprocess and analyze large data sets. This methodical approach not only enhances our current analysis, but also sets a robust statistical foundation for the development of predictive models, which will be the focus of the subsequent paper. In identifying the key determinants that affect the timing of SEP detection, we establish the vital features that will inform the machine-learning (ML) techniques explored in the second paper. There, we will utilize advanced ML models—such as survival trees and random survival forests—to evolve SEP event prediction capabilities. This research is committed to advancing space weather, strengthening the safety of space-borne technology, and safeguarding astronaut health.

Reconciling Legal and Empirical Conceptions of Disparate Impact: An Analysis of Police Stops Across California

We evaluate the statistical and conceptual foundations of empirical tests for disparate impact. We begin by considering a recent, popular proposal in the economics literature that seeks to assess disparate impact via a comparison of error rates for the majority and the minority group. Building on past work, we show that this approach suffers from what is colloquially known as “the problem of inframarginality”, in turn putting it in direct conflict with legal understandings of discrimination. We then analyze two alternative proposals that quantify disparate impact either in terms of risk-adjusted disparities or by comparing existing disparities to those under a statistically optimized decision policy. Both approaches have differing, context-specific strengths and weaknesses, and we discuss how they relate to the individual elements in the legal test for disparate impact. We then turn towards assessing disparate impact of search decisions among approximately 1.5 million police stops recorded across California in 2022 pursuant to its Racial Identity and Profiling Act (RIPA). The results are suggestive of disparate impact against Black and Hispanic drivers for several large law enforcement agencies. We further propose alternative search strategies that more efficiently recover contraband while also exerting fewer racial disparities.

Entropy, Deterministic Chaos, and New Forms of Intelligibility: A Shared Frame of Reference for Physics and Psychology

Prigogine’s theory of dissipative structures provides a general account of entropy-driven self-organized transitions through hierarchies of structures separated by discontinuities. The theory encompasses a wide range of evolving systems throughout nature and culture. Possibilities for operationalizing a new collective rationality spanning physics and psychology emerge from Prigogine’s emphases on two distinct senses of probability, on the concept of the sufficient statistic, and on the role and limitations of the Poisson distribution in formulating a “nonlinear master equation.” Unnoted by Prigogine are correspondences of all three of these issues in the mathematical foundations of statistics and measurement established in the works of Ronald Fisher and his student, Georg Rasch. The three areas of correspondence inform models enabling specifically metrological approaches to quality-assured quantification across the sciences. Prigogine’s sense of “deterministic chaos” is re-expressed in measurement terms as stochastic invariance and the need for “a supplementary parameter” augmenting the Poisson distribution is related to a rating scale model of measurement. In light of these connections, this paper proposes that what Prigogine anticipates as a “new intelligibility” and a new science of “collective rationality” could be pragmatically operationalized in a new metrological infrastructure made coherent by the generality of entropy-driven nonequilibrium processes.

Statistical Approaches to Machine Learning in a Big Data Environment

This thesis explores statistical approaches to machine learning in a big data environment. Firstly, the connections and differences between machine learning and statistics in a big data environment are introduced, as well as the statistical foundations in machine learning models. Secondly, the application of statistical methods in big data analysis is discussed, including the combination of traditional data analysis and machine learning. Then, the challenges and limitations of statistical methods in the big data environment, such as high dimensionality and huge amount of data, are discussed. Then, common statistical methods in the big data environment, including linear regression, decision trees, and support vector machines, are described in detail. Finally, the research findings are summarised and future directions and research trends are outlined. Through the research in this paper, a deeper understanding of statistical methods for machine learning in big data environment is provided, which provides an important reference for big data analysis and application.

The AccelerAge framework: a new statistical approach to predict biological age based on time-to-event data

Aging is a multifaceted and intricate physiological process characterized by a gradual decline in functional capacity, leading to increased susceptibility to diseases and mortality. While chronological age serves as a strong risk factor for age-related health conditions, considerable heterogeneity exists in the aging trajectories of individuals, suggesting that biological age may provide a more nuanced understanding of the aging process. However, the concept of biological age lacks a clear operationalization, leading to the development of various biological age predictors without a solid statistical foundation. This paper addresses these limitations by proposing a comprehensive operationalization of biological age, introducing the “AccelerAge” framework for predicting biological age, and introducing previously underutilized evaluation measures for assessing the performance of biological age predictors. The AccelerAge framework, based on Accelerated Failure Time (AFT) models, directly models the effect of candidate predictors of aging on an individual’s survival time, aligning with the prevalent metaphor of aging as a clock. We compare predictors based on the AccelerAge framework to a predictor based on the GrimAge predictor, which is considered one of the best-performing biological age predictors, using simulated data as well as data from the UK Biobank and the Leiden Longevity Study. Our approach seeks to establish a robust statistical foundation for biological age clocks, enabling a more accurate and interpretable assessment of an individual’s aging status.

A study concept of expeditious clinical enrollment for genetic modifier studies in Charcot-Marie-Tooth neuropathy 1A.

Caused by duplications of the gene encoding peripheral myelin protein 22 (PMP22), Charcot-Marie-Tooth disease type 1A (CMT1A) is the most common hereditary neuropathy. Despite this shared genetic origin, there is considerable variability in clinical severity. It is hypothesized that genetic modifiers contribute to this heterogeneity, the identification of which may reveal novel therapeutic targets. In this study, we present a comprehensive analysis of clinical examination results from 1564 CMT1A patients sourced from a prospective natural history study conducted by the RDCRN-INC (Inherited Neuropathy Consortium). Our primary objective is to delineate extreme phenotype profiles (mild and severe) within this patient cohort, thereby enhancing our ability to detect genetic modifiers with large effects. We have conducted large-scale statistical analyses of the RDCRN-INC database to characterize CMT1A severity across multiple metrics. We defined patients below the 10th (mild) and above the 90th (severe) percentiles of age-normalized disease severity based on the CMT Examination Score V2 and foot dorsiflexion strength (MRC scale). Based on extreme phenotype categories, we defined a statistically justified recruitment strategy, which we propose to use in future modifier studies. Leveraging whole genome sequencing with base pair resolution, a future genetic modifier evaluation will include single nucleotide association, gene burden tests, and structural variant analysis. The present work not only provides insight into the severity and course of CMT1A, but also elucidates the statistical foundation and practical considerations for a cost-efficient and straightforward patient enrollment strategy that we intend to conduct on additional patients recruited globally.

The Significance of Statistics in Artificial Intelligence

Abstract: Artificial intelligence is a fast-expanding subject. The aim of artificial intelligence is to use machine learning and algorithms to build intelligent computers that have human-like thought and behavior. Statistics plays a pivotal role in the development and advancement of Artificial Intelligence. Statistics is a branch of science which deals with study of Collection, Presentation, Analysis and Interpretation of data. Statistical techniques enhance the reliability of Artificial intelligence models and ensure informed decision-making. Combining statistical approaches with Artificial intelligence not only tackles practical issues like bias prevention, uncertainty quantification, and ethical considerations, but also enriches the foundations of theory. This paper aims to investigate the significance of statistics in the field of artificial intelligence. The paper aims to explore the theoretical foundations of Artificial intelligence and Statistics, the statistical methods used in Artificial intelligence, the applications of Statistics in Artificial intelligence, the key points including Statistics in Artificial intelligence, the challenges and limitations, and the prospective path.