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There has long been an impression that reliabilism implies externalism and that frequentist statistics is externalist because it is reliabilist. I argue, however, that frequentist statistics can be plausibly understood as a form of internalist reliabilism -- internalist in the conventional sense but reliabilist in certain unconventional yet intriguing ways. More importantly, I develop the thesis that reliabilism does not imply externalism, not by stretching the meaning of 'reliabilism' merely to break the implication, but in order to better understand frequentist statistics, which represents one of the most sustained attempts by scientists to develop an epistemology for their own use.

In 2017, Hughes claimed an equivalence between Tjurs $R^2$ coefficient of discrimination and Youden index for assessing diagnostic test performance on $2\times 2$ contingency tables. We prove an impossibility result when averaging over binary outcomes (0s and 1s) under any continuous real-valued scoring rule. Our findings clarify the limitations of such a possible equivalence and highlights the distinct roles these metrics play in diagnostic test assessment.

We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.

Patients at a comprehensive cancer center who do not achieve cure or remission following standard treatments often become candidates for clinical trials. Patients who participate in a clinical trial may be suitable for other studies. A key factor influencing patient enrollment in subsequent clinical trials is the structured collaboration between oncologists and most responsible physicians. Possible identification of these collaboration networks can be achieved through the analysis of patient movements between clinical trial intervention types with social network analysis and community detection algorithms. In the detection of oncologist working groups, the present study evaluates three community detection algorithms: Girvan-Newman, Louvain and an algorithm developed by the author. Girvan-Newman identifies each intervention as their own community, while Louvain groups interventions in a manner that is difficult to interpret. In contrast, the author's algorithm groups interventions in a way that is both intuitive and informative, with a gradient evident in social partitioning that is particularly useful for epidemiological research. This lays the groundwork for future subgroup analysis of clustered interventions., Comment: 35 page, 10 figures, 3 tables

Artificial Intelligence (AI) is a field that utilizes computing and often, data and statistics, intensively together to solve problems or make predictions. AI has been evolving with literally unbelievable speed over the past few years, and this has led to an increase in social, cultural, industrial, scientific, and governmental concerns about the ethical development and use of AI systems worldwide. The ASA has issued a statement on ethical statistical practice and AI (ASA, 2024), which echoes similar statements from other groups. Here we discuss the support for ethical statistical practice and ethical AI that has been established in long-standing human rights law and ethical practice standards for computing and statistics. There are multiple sources of support for ethical statistical practice and ethical AI deriving from these source documents, which are critical for strengthening the operationalization of the "Statement on Ethical AI for Statistics Practitioners". These resources are explicated for interested readers to utilize to guide their development and use of AI in, and through, their statistical practice., Comment: 10 pages; Preprint of submission to Proceedings of JSM 2024 Portland, OR

The Stirling approximation formula for $n!$ dates from 1730. Here we give new and instructive proofs of this and related approximation formulae via tools of probability and statistics. There are connections to the Central Limit Theorem and also to approximations of marginal distributions in Bayesian setups. Certain formulae emerge by working through particular instances, some independently verifiable but others perhaps not. A particular case yielding new formulae is that of summing independent uniforms, related to the Irwin--Hall distribution. Yet further proofs of the Stirling flow from examining aspects of limiting normality of the sample median of uniforms, and from these again we find a proof for the Wallis product formula for $\pi$.

Factor Analysis has traditionally been utilized across diverse disciplines to extrapolate latent traits that influence the behavior of multivariate observed variables. Historically, the focus has been on analyzing data from a single study, neglecting the potential study-specific variations present in data from multiple studies. Multi-study factor analysis has emerged as a recent methodological advancement that addresses this gap by distinguishing between latent traits shared across studies and study-specific components arising from artifactual or population-specific sources of variation. In this paper, we extend the current methodologies by introducing novel shrinkage priors for the latent factors, thereby accommodating a broader spectrum of scenarios -- from the absence of study-specific latent factors to models in which factors pertain only to small subgroups nested within or shared between the studies. For the proposed construction we provide conditions for identifiability of factor loadings and guidelines to perform straightforward posterior computation via Gibbs sampling. Through comprehensive simulation studies, we demonstrate that our proposed method exhibits competing performance across a variety of scenarios compared to existing methods, yet providing richer insights. The practical benefits of our approach are further illustrated through applications to bird species co-occurrence data and ovarian cancer gene expression data.

Undergraduate graders are frequently important contributors to the teaching team in post-secondary education settings. This study set out to investigate agreement for a team of undergraduate graders as they acquired training and experience for scoring responses to open-ended tasks. Results demonstrate compelling evidence that undergraduate students can develop the ability to establish and sustain substantial agreement with an instructor, especially when equipped with proper training and a high-quality scoring rubric., Comment: Supplemental materials for the preprint available by request from the first author

Psychometrics and quantitative psychology rely strongly on statistical models to measure psychological processes. As a branch of mathematics, geometry is inherently connected to measurement and focuses on properties such as distance and volume. However, despite the common root of measurement, geometry is currently not used a lot in psychological measurement. In this paper, my aim is to illustrate how ideas from non-Euclidean geometry may be relevant for psychometrics.

In using observed data to make inferences about a population quantity, it is commonly assumed that the sampling distribution from which the data were drawn belongs to a given parametric family of distributions, or at least, a given finite set of such families, i.e. the population space is assumed to be closed. Here, we address the problem of how to determine an appropriate post-data distribution for a given population quantity when such an assumption about the underlying sampling distribution is not made, i.e. when the population space is open. The strategy used to address this problem is based on the fact that even though, due to an open population space being non-measurable, we are not able to place a post-data distribution over all the sampling distributions contained in such a population space, it is possible to partition this type of space into a finite, countable or uncountable number of subsets such that a distribution can be placed over a variable that simply indicates which of these subsets contains the true sampling distribution. Moreover, it is argued that, by using sampling distributions that belong to a number of parametric families, it is possible to adequately and elegantly represent the sampling distributions that belong to each of the subsets of such a partition. Since a statistical model is conceived as being a model of a population space rather than a model of a sampling distribution, it is also argued that neither the type of models that are put forward nor the expression of pre-data knowledge via such models can be directly brought into question by the data. Finally, the case is made that, as well as not being required in the modelling process that is proposed, the standard practice of using P values to measure the absolute compatibility of an individual or family of sampling distributions with observed data is neither meaningful nor useful., Comment: Possibly the final version

In recent years, self-starting methods have garnered increasing attention in Statistical Process Control and Monitoring (SPC/M), as they offer real-time disorder detection without the need for a calibration phase (Phase I). This study focuses on evaluating parametric self-starting CUSUM-type control charts, specifically the Bayesian Predictive Ratio CUSUM (PRC) developed by Bourazas et al. (2023) and the frequentist alternative self-starting CUSUM proposed by Hawkins and Olwell (1998). The performance of these methods is thoroughly examined through an extensive simulation study under various scenarios involving a change in the mean of Normal data. Additionally, a prior sensitivity analysis for PRC is conducted. The work ands with concluding remarks summarizing the findings.

This article reviews and develops an epistemological tradition in philosophy of science, called convergentism, which holds that inference methods should be assessed in terms of their abilities to converge to the truth. This tradition is compared with three competing ones: (1) explanationism, which holds that theory choice should be guided by a theory's overall balance of explanatory virtues, such as simplicity and fit with data; (2) instrumentalism, according to which scientific inference should be driven by the goal of obtaining useful models, rather than true theories; (3) Bayesianism, which features a shift of focus from all-or-nothing beliefs to degrees of belief.

A comprehensive review of the literature on crossover design is needed to highlight its evolution, applications, and methodological advancements across various fields. Given its widespread use in clinical trials and other research domains, understanding this design's challenges, assumptions, and innovations is essential for optimizing its implementation and ensuring accurate, unbiased results. This article extensively reviews the history and statistical inference methods for crossover designs. A primary focus is given to the AB-BA design as it is the most widely used design in literature. Extension from two periods to higher-order designs is discussed, and a general inference procedure for continuous response is studied. Analysis of multivariate and categorical responses is also reviewed in this context. A bunch of open problems in this area are shortlisted.

The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary has been the focus of scholarship in existing literature on the linguistics of mathematics and statistics but there are structures that go beyond the content of words and symbols. Here I introduce ideas for grammar and discourse features through a sequence of examples.

Motivation Network visualization is critical for effective communication in various fields of knowledge. Currently, a gap separates network manipulation from network visualization in programming environments. Users often export network data to be laid out in external interactive software, like Cytoscape and Gephi. We argue the current R package ecosystem lacks an interactive layout engine well integrated with common data analysis workflows. Results We present easylayout, an R package that bridges network manipulation and visualization by leveraging interactive force simulations within the IDE itself (e.g., RStudio, VSCode). It is not yet another visualization library, but instead aims to interconnect existing libraries and streamline their usage into the R ecosystem. easylayout takes an igraph object and serializes it into a web application integrated with the IDE's interface through a Shiny server. The app lays out the network by simulating attraction and repulsion forces. Simulation parameters can be adjusted in real-time. An editing mode allows moving and rotating nodes. The implementation aims for performance, so that even lower-end devices are able to work with relatively large networks. Once the user finishes tweaking the layout, it is sent back to the R session to be plotted through popular libraries like ggraph, igraph or even the base package itself. The current implementation focuses on the R ecosystem, but using web technologies makes it easily portable to similar environments, like Python/Jupyter Notebooks. We expect this tool to reduce the time spent searching for suitable network layouts, ultimately allowing researchers to generate more compelling figures. Availability and implementation easylayout is freely available under an MIT license on GitHub (https://github.com/dalmolingroup/easylayout). The package is implemented in R/Shiny and JavaScript/Svelte.

Carlsson, Singh and Memoli's TDA mapper takes a point cloud dataset and outputs a graph that depends on several parameter choices. Dey, Memoli, and Wang developed Multiscale Mapper for abstract topological spaces so that parameter choices can be analyzed via persistent homology. However, when applied to actual data, one does not always obtain filtrations of mapper graphs. DBSCAN, one of the most common clustering algorithms used in the TDA mapper software, has two parameters, \textbf{$\epsilon$} and \textbf{MinPts}. If \textbf{MinPts = 1} then DBSCAN is equivalent to single linkage clustering with cutting height \textbf{$\epsilon$}. We show that if DBSCAN clustering is used with \textbf{MinPts $>$ 2}, a filtration of mapper graphs may not exist except in the absence of free-border points; but such filtrations exist if DBSCAN clustering is used with \textbf{MinPts = 1} or \textbf{2} as the cover size increases, \textbf{$\epsilon$} increases, and/or \textbf{MinPts} decreases. However, the 1-dimensional filtration is unstable. If one adds noise to a data set so that each data point has been perturbed by a distance at most \textbf{$\delta$}, the persistent homology of the mapper graph of the perturbed data set can be significantly different from that of the original data set. We show that we can obtain stability by increasing both the cover size and \textbf{$\epsilon$} at the same time. In particular, we show that the bi-filtrations of the homology groups with respect to cover size and $\epsilon$ between these two datasets are \textbf{2$\delta$}-interleaved.

We explore the application of uncertainty quantification methods to agent-based models (ABMs) using a simple sheep and wolf predator-prey model. This work serves as a tutorial on how techniques like emulation can be powerful tools in this context. We also highlight the importance of advanced statistical methods in effectively utilising computationally expensive ABMs. Specifically, we implement stochastic Gaussian processes, Gaussian process classification, sequential design, and history matching to address uncertainties in model input parameters and outputs. Our results show that these methods significantly enhance the robustness, accuracy, and predictive power of ABMs.

Oral exams are a powerful tool for educators to gauge student's learning. This is particularly important in introductory statistics classes where many students struggle to grasp a deep meaning of topics like $p$-values, confidence intervals, hypothesis testing, and more. These challenges are only heightened in a context where students are learning in a second language. In this paper, I share my experience administering oral exams to an introductory statistics class of non-native English speakers at a Japanese university. I explain the context of the university and course that the exam was given in, before sharing details about the two exams. Despite the challenges the students (and I myself) faced, the exams seemed to truly test their statistical knowledge and not merely their English proficiency, as I found little relationship between a student's English ability and performance. I close with encouragements and recommendations for practitioners hoping to implement these exams, all while keeping an eye towards the unique difficulties faced by students not learning in their mother tongue.

We present a de Bruijn type approximation for quantifying the content of m smooth numbers, derived from samples obtained through a probability measure over the set of integers less than or equal to n, with point mass function at k inversely proportional to k. Our analysis is based on a stochastic representation of the measure of interest, utilizing weighted independent geometric random variables. This representation is analyzed through the lens of Stein method for the Dickman distribution. A pivotal element of our arguments relies on precise estimations concerning the regularity properties of the solution to the Dickman Stein equation for heaviside functions, recently developed by Bhattacharjee and Schulte. Remarkably, our arguments remain mostly in the realm of probability theory, with Mertens first and third theorems standing as the only number theory estimations required.

This study introduces a correction to the approximation of effective degrees of freedom as proposed by Satterthwaite (1941, 1946), specifically addressing scenarios where component degrees of freedom are small. The correction is grounded in analytical results concerning the moments of standard normal random variables. This modification is applicable to complex variance estimates that involve both small and large degrees of freedom, offering an enhanced approximation of the higher moments required by Satterthwaite's framework. Additionally, this correction extends and partially validates the empirically derived adjustment by Johnson & Rust (1992), as it is based on theoretical foundations rather than simulations used to derive empirical transformation constants.

Integration of probabilistic and non-probabilistic samples for the estimation of finite population totals (or means) has recently received considerable attention in the field of survey sampling; yet, to the best of our knowledge, this framework has not been extended to cumulative distribution function (CDF) estimation. To address this gap, we propose a novel CDF estimator that integrates data from probability samples with data from (potentially large) nonprobability samples. Assuming that a set of shared covariates are observed in both samples, while the response variable is observed only in the latter, the proposed estimator uses a survey-weighted empirical CDF of regression residuals trained on the convenience sample to estimate the CDF of the response variable. Under some regularity conditions, we show that our CDF estimator is both design-consistent for the finite population CDF and asymptotically normally distributed. Additionally, we define and study a quantile estimator based on the proposed CDF estimator. Furthermore, we use both the bootstrap and asymptotic formulae to estimate their respective sampling variances. Our empirical results show that the proposed CDF estimator is robust to model misspecification under ignorability, and robust to ignorability under model misspecification. When both assumptions are violated, our residual-based CDF estimator still outperforms its 'plug-in' mass imputation and naive siblings, albeit with noted decreases in efficiency.

Success in todays data-driven corporate climate requires a deep understanding of employee behavior. Companies aim to improve employee satisfaction, boost output, and optimize workflow. This research study delves into creating synthetic data, a powerful tool that allows us to comprehensively understand employee performance, flexibility, cooperation, and team dynamics. Synthetic data provides a detailed and accurate picture of employee activities while protecting individual privacy thanks to cutting-edge methods like agent-based models (ABMs), Generative Adversarial Networks (GANs), and statistical models. Through the creation of multiple situations, this method offers insightful viewpoints regarding increasing teamwork, improving adaptability, and accelerating overall productivity. We examine how synthetic data has evolved from a specialized field to an essential resource for researching employee behavior and enhancing management efficiency. Keywords: Agent-Based Model, Generative Adversarial Network, workflow optimization, organizational success, Comment: 8 Pages, 5 figures, 1 github link

This paper investigates the problem of adaptive detection of distributed targets in power heterogeneous clutter. In the considered scenario, all the data share the identical structure of clutter covariance matrix, but with varying and unknown power mismatches. To address this problem, we iteratively estimate all the unknowns, including the coordinate matrix of the target, the clutter covariance matrix, and the corresponding power mismatches, and propose three detectors based on the generalized likelihood ratio test (GLRT), Rao and the Wald tests. The results from simulated and real data both illustrate that the detectors based on GLRT and Rao test have higher probabilities of detection (PDs) than the existing competitors. Among them, the Rao test-based detector exhibits the best overall detection performance. We also analyze the impact of the target extended dimensions, the signal subspace dimensions, and the number of training samples on the detection performance. Furthermore, simulation experiments also demonstrate that the proposed detectors have a constant false alarm rate (CFAR) property for the structure of clutter covariance matrix., Comment: 9 pages, 11 figures. This manuscript is accepted in IEEE Sensors Journal

In this thesis, we consider an $N$-dimensional Ornstein-Uhlenbeck (OU) process satisfying the linear stochastic differential equation $d\mathbf x(t) = - \mathbf B\mathbf x(t) dt + \boldsymbol \Sigma d \mathbf w(t).$ Here, $\mathbf B$ is a fixed $N \times N$ circulant friction matrix whose eigenvalues have positive real parts, $\boldsymbol \Sigma$ is a fixed $N \times M$ matrix. We consider a signal propagation model governed by this OU process. In this model, an underlying signal propagates throughout a network consisting of $N$ linked sensors located in space. We interpret the $n$-th component of the OU process as the measurement of the propagating effect made by the $n$-th sensor. The matrix $\mathbf B$ represents the sensor network structure: if $\mathbf B$ has first row $(b_1 \ , \ \dots \ , \ b_N),$ where $b_1>0$ and $b_2 \ , \ \dots \ ,\ b_N \le 0,$ then the magnitude of $b_p$ quantifies how receptive the $n$-th sensor is to activity within the $(n+p-1)$-th sensor. Finally, the $(m,n)$-th entry of the matrix $\mathbf D = \frac{\boldsymbol \Sigma \boldsymbol \Sigma^\text T}{2}$ is the covariance of the component noises injected into the $m$-th and $n$-th sensors. For different choices of $\mathbf B$ and $\boldsymbol \Sigma,$ we investigate whether Cyclicity Analysis enables us to recover the structure of network. Roughly speaking, Cyclicity Analysis studies the lead-lag dynamics pertaining to the components of a multivariate signal. We specifically consider an $N \times N$ skew-symmetric matrix $\mathbf Q,$ known as the lead matrix, in which the sign of its $(m,n)$-th entry captures the lead-lag relationship between the $m$-th and $n$-th component OU processes. We investigate whether the structure of the leading eigenvector of $\mathbf Q,$ the eigenvector corresponding to the largest eigenvalue of $\mathbf Q$ in modulus, reflects the network structure induced by $\mathbf B.$, Comment: Ph.D. thesis successfully defended and deposited in July 2024. To appear in the IDEALS repository

Heavy-tailed distributions, such as the Cauchy distribution, are acknowledged for providing more accurate models for financial returns, as the normal distribution is deemed insufficient for capturing the significant fluctuations observed in real-world assets. Data sets characterized by outlier sensitivity are critically important in diverse areas, including finance, economics, telecommunications, and signal processing. This article addresses a goodness-of-fit test for the Cauchy distribution. The proposed test utilizes empirical likelihood methods, including the jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL). Extensive Monte Carlo simulation studies are conducted to evaluate the finite sample performance of the proposed test. The application of the proposed test is illustrated through the analysing two real data sets., Comment: 15 pages

This study introduces a novel approach to forecasting by Tobit Exponential Smoothing with time aggregation constraints. This model, a particular case of the Tobit Innovations State Space system, handles censored observed time series effectively, such as sales data, with known and potentially variable censoring levels over time. The paper provides a comprehensive analysis of the model structure, including its representation in system equations and the optimal recursive estimation of states. It also explores the benefits of time aggregation in state space systems, particularly for inventory management and demand forecasting. Through a series of case studies, the paper demonstrates the effectiveness of the model across various scenarios, including hourly and daily censoring levels. The results highlight the model's ability to produce accurate forecasts and confidence bands comparable to those from uncensored models, even under severe censoring conditions. The study further discusses the implications for inventory policy, emphasizing the importance of avoiding spiral-down effects in demand estimation. The paper concludes by showcasing the superiority of the proposed model over standard methods, particularly in reducing lost sales and excess stock, thereby optimizing inventory costs. This research contributes to the field of forecasting by offering a robust model that effectively addresses the challenges of censored data and time aggregation., Comment: 18 pages, 6 figures, 2 tables

In this paper, we consider how probability theory can be used to determine the survival strategy in two of the ``Squid Game" and ``Squid Game: The Challenge" challenges: the Hopscotch and the Warships. We show how Hopscotch can be easily tackled with the knowledge of the binomial distribution, taught in introductory statistics courses, while Warships is a much more complex problem, which can be tackled at different levels., Comment: 10 pages, 5 figures

This letter presents simple analytical expressions for the spatial and temporal correlation functions in channels with von Mises-Fisher (vMF) scattering. In contrast to previous results, the expressions presented here are exact and based only on elementary functions, clearly revealing the impact of the underlying parameters. The derived results are validated by a comparison against numerical integration result, where an exact match is observed. To demonstrate their utility, the presented results are used to analyze spatial correlation across different antenna array geometries and to investigate temporal correlation of a fluctuating radar signal from a moving target., Comment: Submitted to IEEE Wireless Communications Letters (submitted on 2024-05-14; revised and resubmitted on 2024-08-26)

This paper presents an analytical analysis of the Doppler spectrum in von Mises-Fisher (vMF) scattering channels. A closed-form expression for the Doppler spectrum is derived and used to investigate the impact of vMF scattering parameters, i.e., the mean direction and the degree of concentration of scatterers. The spectrum is observed to exhibit exponential behavior for the mobile antenna motion parallel to the mean direction of scatterers, while conforming to a Gaussian-like shape for the perpendicular motion. The validity of the obtained results is verified by comparison against the results of Monte Carlo simulations, where an exact match is observed., Comment: Submitted to IEEE Communications Letters (submitted on 2024-07-26)

While research on adolescent smoking is extensive, little attention has been given to smoking behaviors among rural middle-aged and older adults. This study examines the role of personal networks and sociodemographic factors in predicting smoking status in a rural Romanian community. Using a link-tracing sampling method, we gathered data from 76 participants out of 83 in Leresti, Arges County. Face-to-face interviews collected sociodemographic data and network information, including smoking status and relational dynamics. We applied multilevel logistic regression models to predict smoking behaviors (current smokers, former smokers, and non-smokers) based on individual characteristics and network influences. Results indicate that social networks significantly influence smoking behaviors. For current smokers, having a smoking family member greatly increased the odds of smoking (OR = 2.51, 95% CI: 1.62, 3.91, p < 0.001). Similarly, non-smoking family members increased the likelihood of being a non-smoker (OR = 1.64, 95% CI: 1.04, 2.61, p < 0.05). Women were less likely to smoke, highlighting sex differences in behavior. These findings emphasize the critical role of social networks in shaping smoking habits, advocating for targeted interventions in rural areas., Comment: 27 pages; 1 figure; 6 tables

The dynamics of information diffusion in complex networks is widely studied in an attempt to understand how individuals communicate and how information travels and reaches individuals through interactions. However, complex networks often present community structure, and tools to analyse information diffusion on networks with communities are needed. In this paper, we develop theoretical tools using multi-type branching processes to model and analyse simple contagion information spread on a broad class of networks with community structure. We show how, by using limited information about the network -- the degree distribution within and between communities -- we can calculate standard statistical characteristics of the dynamics of information diffusion, such as the extinction probability, hazard function, and cascade size distribution. These properties can be estimated not only for the entire network but also for each community separately. Furthermore, we estimate the probability of information spreading from one community to another where it is not currently spreading. We demonstrate the accuracy of our framework by applying it to two specific examples: the Stochastic Block Model and a log-normal network with community structure. We show how the initial seeding location affects the observed cascade size distribution on a heavy-tailed network and that our framework accurately captures this effect.

The weighted kappa coefficient of a binary diagnostic test is a measure of the beyond-chance agreement between the diagnostic test and the gold standard, and depends on the sensitivity and specificity of the diagnostic test, on the disease prevalence and on the relative importance between the false positives and the false negatives. This article studies the comparison of the weighted kappa coefficients of two binary diagnostic tests subject to a paired design through confidence intervals. Three asymptotic confidence intervals are studied for the difference between the parameters and five other intervals for the ratio. Simulation experiments were carried out to study the coverage probabilities and the average lengths of the intervals, giving some general rules for application. A method is also proposed to calculate the sample size necessary to compare the two weighted kappa coefficients through a confidence interval. A program in R has been written to solve the problem studied and it is available as supplementary material. The results were applied to a real example of the diagnosis of malaria., Comment: 43 pages, 10 tables

Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are equivalent to a relative risk. This article studies the comparison of the likelihood ratios of two binary diagnostic tests subject to a paired design through confidence intervals. Six approximate confidence intervals are presented for the ratio of the likelihood ratios, and simulation experiments are carried out to study the coverage probabilities and the average lengths of the intervals considered, and some general rules of application are proposed. A method is also proposed to determine the sample size necessary to estimate the ratio between the likelihood ratios with a determined precision. The results were applied to the diagnosis of coronary artery disease., Comment: 35 pages, 7 tables

Predictive values are measures of the clinical accuracy of a binary diagnostic test, and depend on the sensitivity and the specificity of the test and on the disease prevalence among the population being studied. This article studies hypothesis tests to simultaneously compare the predictive values of two binary diagnostic tests in the presence of missing data. The hypothesis tests were solved applying two computational methods: the EM and SEM algorithms and multiple imputation. Simulation experiments were carried out to study the sizes and the power of the hypothesis tests, giving some general rules of application. Two R programmes were written to apply each method, and they are available as supplementary material for the manuscript. The results were applied to the diagnosis of Alzheimer's disease., Comment: 47 pages, 7 tables

Foreigners and "estrangeirados", an expression meaning "people going to a foreign country ["estrangeiro"] getting there further education", had a leading role in the development of Mathematical Statistics in Portugal. In what concerns Statistics, "estrangeirados" in the nineteenth century were mainly liberal intellectuals exiled for political reasons. From 1930 onwards, the research funding authority sent university professors abroad, and hired foreign researchers to stay in Portuguese institutions, and some of them were instrumental in the importation of new concepts and methods of inferential statistics. After 1970, there was a huge program of sending young researchers abroad for doctoral studies. At the same time, many new universities and polytechnic institutes have been created in Portugal. After that, aside from foreigners who choose to have a research career in those institutions and the "estrangeirados" who had returned and created programs of doctoral studies, others, who hadn't the opportunity of studying abroad, began to play a decisive role in the development of Statistics in Portugal. The publication of handbooks on Probability and Statistics, thesis and core papers in Portuguese scientific journals, and also of works for the layman, reveals how Statistics progressed from descriptive to a mathematical discipline used for inference in all fields of knowledge, from natural sciences to methodology of scientific research., Comment: 67 pages, 34 figures

We undertake extensive analysis of English Premier League data over the period 2009/10 to 2017/18 to identify and rank key factors affecting the economic and footballing performances of the teams. Alternative end-of-season league tables are generated by re-ranking the teams based on five different descriptors - total expenditure, total funds spent on players, total funds spent on foreign players, the ratio of foreign to British players and the overall profit. The unequal distribution of resources and expenditure between the clubs is analyzed through Lorenz curves. A comparative analysis of the differences between the alternative tables and the conventional end-of-season league table establishes the most likely factors to influence the performances of the teams that we also rank using Principal Component Analysis. We find that the top teams in the league are also those that tend to have the highest expenditure overall, for all players, including foreign players; they also have the highest ratios of foreign to British players. Our statistical and machine learning study also indicates that successful performance on the field may not guarantee healthy profits at the end of the season., Comment: Graphical Abstract & 8 figures in the main text, 3 Appendices with additional figures and tables

An approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows to construct missingness indicators in a flexible and principled way via copulas and Bernoulli margins and to incorporate dependence in missingness patterns. Besides more classical missingness models such as missing completely at random, missing at random, and missing not at random, the approach is able to model structured missingness such as block missingness and, via mixtures, monotone missingness, which are patterns of missing data frequently found in real-life datasets. Properties such as joint missingness probabilities or missingness correlation are derived mathematically. The approach is demonstrated with mathematical examples and empirical illustrations in terms of a well-known dataset.

In inference problems, we often have domain knowledge which allows us to define summary statistics that capture most of the information content in a dataset. In this paper, we present a hybrid approach, where such physics-based summaries are augmented by a set of compressed neural summary statistics that are optimised to extract the extra information that is not captured by the predefined summaries. The resulting statistics are very powerful inputs to simulation-based or implicit inference of model parameters. We apply this generalisation of Information Maximising Neural Networks (IMNNs) to parameter constraints from tomographic weak gravitational lensing convergence maps to find summary statistics that are explicitly optimised to complement angular power spectrum estimates. We study several dark matter simulation resolutions in low- and high-noise regimes. We show that i) the information-update formalism extracts at least $3\times$ and up to $8\times$ as much information as the angular power spectrum in all noise regimes, ii) the network summaries are highly complementary to existing 2-point summaries, and iii) our formalism allows for networks with smaller, physically-informed architectures to match much larger regression networks with far fewer simulations needed to obtain asymptotically optimal inference., Comment: 16 pages, 11 figures. Submitted to JCAP. We provide publicly available code at https://github.com/tlmakinen/hybridStatsWL

Polychoric correlation is often an important building block in the analysis of rating data, particularly for structural equation models. However, the commonly employed maximum likelihood (ML) estimator is highly susceptible to misspecification of the polychoric correlation model, for instance through violations of latent normality assumptions. We propose a novel estimator that is designed to be robust to partial misspecification of the polychoric model, that is, the model is only misspecified for an unknown fraction of observations, for instance (but not limited to) careless respondents. In contrast to existing literature, our estimator makes no assumption on the type or degree of model misspecification. It furthermore generalizes ML estimation, is consistent as well as asymptotically normally distributed, and comes at no additional computational cost. We demonstrate the robustness and practical usefulness of our estimator in simulation studies and an empirical application on a Big Five administration. In the latter, the polychoric correlation estimates of our estimator and ML differ substantially, which, after further inspection, is likely due to the presence of careless respondents that the estimator helps identify., Comment: 50 pages (30 main text), 13 figures (8 in main text), 9 tables (4 in main text). Changes to v2: minor adjustments to simulation designs. arXiv admin note: text overlap with arXiv:2403.11954

A recent original line of research in time--frequency analysis has shifted the interest in energy maxima toward zeros. Initially motivated by the intriguing uniform spread of the zeros of the spectrogram of white noise, it has led to fruitful theoretical developments combining probability theory, complex analysis and signal processing. In this vein, the present work proposes a characterization of the zeros of the Stockwell Transform of white noise, which consists in an hybrid time--frequency multiresolution representation. First of all, an analytic version of the Stockwell Transform is designed. Then, analyticity is leveraged to establish a connection with the hyperbolic Gaussian Analytic Function, whose zero set is invariant under the isometries of the Poincar\'e disk. Finally, the theoretical spatial statistics of the zeros of the hyperbolic Gaussian Analytic Function and the empirical statistics of the zeros the Analytic Stockwell Transform of white noise are compared through intensive Monte Carlo simulations, supporting the established connection. A publicly available documented Python toolbox accompanies this work.

Psychological research often involves understanding psychological constructs through conducting factor analysis on data collected by a questionnaire, which can comprise hundreds of questions. Without interactive systems for interpreting factor models, researchers are frequently exposed to subjectivity, potentially leading to misinterpretations or overlooked crucial information. This paper introduces FAVis, a novel interactive visualization tool designed to aid researchers in interpreting and evaluating factor analysis results. FAVis enhances the understanding of relationships between variables and factors by supporting multiple views for visualizing factor loadings and correlations, allowing users to analyze information from various perspectives. The primary feature of FAVis is to enable users to set optimal thresholds for factor loadings to balance clarity and information retention. FAVis also allows users to assign tags to variables, enhancing the understanding of factors by linking them to their associated psychological constructs. Our user study demonstrates the utility of FAVis in various tasks., Comment: 5 pages and 2 figures. To Appear in IEEE VIS 2024

By conducting a bibliometric analysis on 4,869 publications in Current Psychology from 2013 to 2022, this paper examined the annual publications and annual citations, as well as the leading institutions, countries, and keywords. CiteSpace, VOSviewer and SCImago Graphica were utilized for visualization analysis. On one hand, this paper analyzed the academic influence of Current Psychology over the past decade. On the other hand, it explored the research hotspots and future development trends within the field of international psychology. The results revealed that the three main research areas covered in the publications of Current Psychology were: the psychological well-being of young people, the negative emotions of adults, and self-awareness and management. The latest research hotspots highlighted in the journal include negative emotions, personality, and mental health. The three main development trends of Current Psychology are: 1) exploring the personality psychology of both adolescents and adults, 2) promoting the interdisciplinary research to study social psychological issues through the use of diversified research methods, and 3) emphasizing the emotional psychology of individuals and their interaction with social reality, from a people-oriented perspective.

In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is constructed through an optimization problem described by the Maximum Mean Discrepancy loss function, which matches the expectation information of the approximated posterior and reference posterior. The proposed method inherits the accurate estimation of the posterior distribution from particle filtering. To improve the robustness of Maximum Mean Discrepancy, a variance penalty term is used to guide the optimization. It prioritizes minimizing the discrepancy between the expectations of highly informative statistics for the approximated and reference posteriors. The penalty term significantly enhances the robustness of the proposed method and leads to a better approximation of the posterior. A few numerical examples are presented to illustrate the advantage of the proposed method over the ensemble Kalman filter., Comment: 27 pages, 14 figures

The definition of Data Science is a hotly debated topic. For many, the definition is a simple shortcut to Artificial Intelligence or Machine Learning. However, there is far more depth and nuance to the field of Data Science than a simple shortcut can provide. The School of Data Science at the University of Virginia has developed a novel model for the definition of Data Science. This model is based on identifying a unified understanding of the data work done across all areas of Data Science. It represents a generational leap forward in how we understand and teach Data Science. In this paper we will present the core features of the model and explain how it unifies various concepts going far beyond the analytics component of AI. From this foundation we will present our Undergraduate Major curriculum in Data Science and demonstrate how it prepares students to be well-rounded Data Science team members and leaders. The paper will conclude with an in-depth overview of the Foundations of Data Science course designed to introduce students to the field while also implementing proven STEM oriented pedagogical methods. These include, for example, specifications grading, active learning lectures, guest lectures from industry experts and weekly gamification labs., Comment: 12 pages, 5 figures, publish at the 53rd Annual Southeast Decision Science Institute 2024, won best paper for Innovation track

For a sequence of $n$ random variables taking values $0$ or $1$, the hot hand statistic of streak length $k$ counts what fraction of the streaks of length $k$, that is, $k$ consecutive variables taking the value $1$, among the $n$ variables are followed by another $1$. Since this statistic does not use the expected value of how many streaks of length $k$ are observed, but instead uses the realization of the number of streaks present in the data, it may be a biased estimator of the conditional probability of a fixed random variable taking value $1$ if it is preceded by a streak of length $k$, as was first studied and observed explicitly in [Miller and Sanjurjo, 2018]. In this short note, we suggest an alternative proof for an explicit formula of the expectation of the hot hand statistic for the case of streak length one. This formula was obtained through a different argument in [Miller and Sanjurjo, 2018] and [Rinott and Bar-Hillel, 2015]., Comment: 4 pages

This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and elegant, accessible to anyone with basic knowledge of calculus, revealing that the law originates from the basic property of the human number system. The criterion can bring great convenience to the field of fraud detection., Comment: 5 latex pages, 1 figure, final version for publication with published pages in journal revised

In a decision problem, observations are said to be material if they must be taken into account to perform optimally. Decision problems have an underlying (graphical) causal structure, which may sometimes be used to evaluate certain observations as immaterial. For soluble graphs - ones where important past observations are remembered - there is a complete graphical criterion; one that rules out materiality whenever this can be done on the basis of the graphical structure alone. In this work, we analyse a proposed criterion for insoluble graphs. In particular, we prove that some of the conditions used to prove immateriality are necessary; when they are not satisfied, materiality is possible. We discuss possible avenues and obstacles to proving necessity of the remaining conditions.

This paper introduces a novel course design in the Master Program in Biostatistics at the University of Zurich that integrates computing skills, effective communication, reproducibility, and scientific integrity within one course. Utilizing a flipped classroom model, the course aims to equip students with the necessary competencies to handle real-world data analysis challenges and effective statistical practice in general. The curriculum includes practical tools such as version control with Git, dynamic reporting, unit testing and containerization to foster reproducibility, and integrity in statistical practice. Feedback gathered from both staff and students post-implementation indicates that the course significantly enhances student readiness for professional and academic environments, demonstrating the effectiveness of this educational approach.

As survey methods adapt to technological and societal changes, a growing body of research seeks to understand the tradeoffs associated with various sampling methods and administration modes. We show how the NSF-funded 2022 Collaborative Midterm Survey (CMS) can be used as a dynamic and transparent framework for evaluating which sampling approaches - or combination of approaches - are best suited for various research goals. The CMS is ideally suited for this purpose because it includes almost 20,000 respondents interviewed using two administration modes (phone and online) and data drawn from random digit dialing, random address-based sampling, a probability-based panel, two nonprobability panels, and two nonprobability marketplaces. The analysis considers three types of population benchmarks (election data, administrative records, and large government surveys) and focuses on the national-level estimates as well as oversamples in three states (California, Florida, and Wisconsin). In addition to documenting how each of the survey strategies performed, we develop a strategy to assess how different combinations of approaches compare to different population benchmarks in order to guide researchers combining sampling methods and sources. We conclude by providing specific recommendations to public opinion and election survey researchers and demonstrating how our approach could be applied to a large government survey conducted at regular intervals to provide ongoing guidance to researchers, government, businesses, and nonprofits regarding the most appropriate survey sampling and administration methods.

Serious traffic congestion and emission by excessive usage of private cars are crucial issues in our modern society. As one solution for these, a concept of Park-and-Ride (PnR) where people stop their private cars (i.e. single-occupancy vehicles) at stations and ride on public vehicles (i.e. mass transportation) are receiving wide attention recently. In this paper, we propose a comprehensive mathematical model which can evaluate waiting times and traveling times of customers, and the total emission of vehicles for various usage ratio of PnR and operation policies of public transportation. Using a system of queues integrated with an emissions model we perform a case-study of Tsukuba city, in Japan. We indicate an intriguing trade-off between the waiting time of customers for the PnR and the long traveling time due to the traffic congestion (leading to high emissions) caused by private cars depending on the usage ratio through some numerical experiments. Moreover, we study the total cost to society caused by total trip times and pollution, in which the decision variables are the capacities and frequencies of the public transportation for the PnR system. Our numerical results showed a significant reduction in the total social cost under the optimal transit policy for the current high usage rate of single-occupancy vehicles. Furthermore, we show that further reduction in the total social cost can be revealed by considering the reduction on the use of private cars compared to the current state implying the social importance of promoting car-free movement., Comment: 52 pages, 35 figures