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arXiv2026

Teachable normal approximations to binomial and related probabilities or confidence bounds

For the usual normal approximations to binomial, hypergeometric, or Poisson interval probabilities, we collect some simple but then reasonably sharp error bounds. For the Clopper-Pearson~(1934) binomial confidence bounds, we present, following Michael Short's~(2023) approach, bounds similar to, but necessarily more complicated than, Lagrange's (1776) success rate plus/minus normal quantile times estimated standard deviation. The bounds, as presented here in four theorems, should be teachable, to people ranging from sufficiently advanced high school pupils to university students in mathematics or statistics: For understanding most of the proposed approximation results, it should suffice to know binomial laws, their means and variances, and the standard normal distribution function, but not necessarily the concept of a corresponding normal random variable. Accompanying technical remarks, references, and proofs are meant for assuring teachers or for stimulating further research. Of the proposed approximations, some are essentially well-known at least to experts, and some are based on teaching experience and research at Trier University.

stat.OT↗

arXiv2025

The Principle of Redundant Reflection

The fact that redundant information does not update a rational belief implies that rational beliefs are updated using Bayes rule. In the framework of Hild (1998a), this is true under mild conditions for discrete, continuous, and arbitrary measure spaces. We prove this result and illustrate it with two examples.

stat.ME↗

arXiv2025

Statistics at a Crossroads; Who is for the Challenge?

This project was sponsored by the National Science Foundation and organized by a steering committee and a group of theme leaders. The six-member steering committee, consisting of James Berger, Xuming He, David Madigan, Susan Murphy, Bin Yu, and Jon Wellner, was responsible for the overall planning of the project. This report is designed to be accessible to the wider audience of key stakeholders in statistics and data science, including academic departments, university administration, and funding agencies. After the role and the value of Statistics and Data Science are discussed in Section 1, the report focuses on the two goals related to emerging research and data-driven challenges in applications. Section 2 identifies emerging research topics from the data challenges arising from scientific and social applications, and Section 3 discusses a number of emerging areas in foundational research. How to engage with those data-driven challenges and foster interdisciplinary collaborations is also summarized in the Executive Summary. The third goal of creating a vibrant research community and maintaining an appropriate balance is addressed in Sections 4 (Professional Culture and Community Responsibilities) and 5 (Doctoral Education).

stat.OT↗

arXiv2025

An Anytime Valid Test for Complete Spatial Randomness

A relevant question when analyzing spatial point patterns is that of spatial randomness. More specifically, before any model can be fit to a point pattern a first step is to test the data for departures from complete spatial randomness (CSR). Traditional techniques employ distance or quadrat counts based methods to test for CSR based on batched data. In this paper, we consider the practical scenario of testing for CSR when the data are available sequentially (i.e., online). We present a sequential testing methodology called as {\em PRe-process} that is based on e-values and is a fast, efficient and nonparametric method. Simulation experiments with the truth departing from CSR in two different scenarios show that the method is effective in capturing inhomogeneity over time. Two real data illustrations considering lung cancer cases in the Chorley-Ribble area, England from 1974 - 1983 and locations of earthquakes in the state of Oklahoma, USA from 2000 - 2011 demonstrate the utility of the PRe-process in sequential testing of CSR.

stat.OT↗

arXiv2025

Underreporting of Intimate Partner Violence in Brazil

According to WHO (2013), in general 30% of all women worldwide who have been in a relationship have experienced physical and/or sexual violence by their intimate partner. However, only a small percentage of intimate partner violence (IPV) victims report it to the police. This phenomenon of under-reporting is known as ``dark figure''. This paper aims to investigate the factors associated with the reporting decision of IPV victims to the police in Brazil using the third wave of the ``Pesquisa de Condições Socioeconômicas e Violência Doméstica e Familiar contra a Mulher ($PCSVDF^{Mulher}$)''. Using a bivariate probit regression model with sample selection, we found that older white women, those who do not tolerate domestic violence, and women who have experienced physical violence are more likely to report IPV to the police. In contrast, married women, those with partners who abuse alcohol and those who witnessed or knew that their mothers had experienced IPV, are less likely to report it to law enforcement.

econ.GN↗

arXiv2025

Communicating complex statistical models to a public health audience: translating science into action with the FARSI approach

Background. Effectively communicating complex statistical model outputs is a major challenge in public health. This study introduces the FARSI approach (Fast, Accessible, Reliable, Secure, Informative) as a framework to enhance the translation of intricate statistical findings into actionable insights for policymakers and stakeholders. We apply this framework in a real-world case study on chronic disease monitoring in Italy. Methods. The FARSI framework outlines key principles for developing user-friendly tools that improve the translation of statistical results. We applied these principles to create an open-access web application using R Shiny, designed to communicate chronic disease prevalence estimates from a Bayesian spatio-temporal logistic model. The case study highlights the importance of an intuitive design for fast accessibility, validated data and expert feedback for reliability, aggregated data for security, and insights into prevalence population subgroups, which were previously unobservable, for informativeness. Results. The web application enables stakeholders to explore disease prevalence across populations and geographical area through dynamic visualizations. It facilitates public health monitoring by, for instance, identifying disparities at the local level and assessing risk factors such as smoking. Its user-friendly interface enhances accessibility, making statistical findings more actionable. Conclusions. The FARSI framework provides a structured approach to improving the communication of complex research findings. By making statistical models more accessible and interpretable, it supports evidence-based decision-making in public health and increases the societal impact of research.

stat.OT↗

arXiv2025

Measures of non-simplifyingness for conditional copulas and vines

In copula modeling, the simplifying assumption has recently been the object of much interest. Although it is very useful to reduce the computational burden, it remains far from obvious whether it is actually satisfied in practice. We propose a theoretical framework which aims at giving a precise meaning to the following question: how non-simplified or close to be simplified is a given conditional copula? For this, we propose a new framework centered at the notion of measure of non-constantness. Then we discuss generalizations of the simplifying assumption to the case where the conditional marginal distributions may not be continuous, and corresponding measures of non-simplifyingness in this case. The simplifying assumption is of particular importance for vine copula models, and we therefore propose a notion of measure of non-simplifyingness of a given copula for a particular vine structure, as well as different scores measuring how non-simplified such a vine decompositions would be for a general vine. Finally, we propose estimators for these measures of non-simplifyingness given an observed dataset. A small simulation study shows the performance of a few estimators of these measures of non-simplifyingness.

math.ST↗

arXiv2026

A roadmap for systematic identification and analysis of multiple biases in causal inference

Observational studies examining causal effects rely on unverifiable assumptions, the violation of which can induce multiple biases. Quantitative bias analysis (QBA) methods examine the sensitivity of findings to such violations, generally, by producing estimates under alternative assumptions, incorporating external information. Although substantial guidance exists for implementing QBA, there is limited guidance on how to systematically determine the assumptions underlying a primary causal analysis and the potential violations that should guide bias analysis. Consequently, many assumptions remain implicit, leading to selective and therefore misleading QBA. To address this gap, we propose a roadmap for systematically identifying and analysing multiple biases. Briefly, this consists of (1) articulating the assumptions underlying the primary analysis through specification and emulation of the ideal trial that defines the causal estimand and depicting these assumptions using a causal diagram; (2) extending the diagram to depict alternative assumptions under which biases may arise; (3) obtaining a single estimate that simultaneously corrects for all potential biases. We illustrate the roadmap using an investigation of the effect of breastfeeding on risk of childhood asthma, and through simulations illustrate the need for analysing multiple biases jointly rather than one at a time.

stat.ME↗

arXiv2025

A conceptual synthesis of causal assumptions for causal discovery and inference

This work presents a conceptual synthesis of causal discovery and inference frameworks, with a focus on how foundational assumptions -- causal sufficiency, causal faithfulness, and the causal Markov condition -- are formalized and operationalized across methodological traditions. Through structured tables and comparative summaries, I map core assumptions, tasks, and analytical choices from multiple causal frameworks, highlighting their connections and differences. The synthesis provides practical guidance for researchers designing causal studies, especially in settings where observational or experimental constraints challenge standard approaches. This guide spans all phases of causal analysis, including question formulation, formalization of background knowledge, selection of appropriate frameworks, choice of study design or algorithm, and interpretation. It is intended as a tool to support rigorous causal reasoning across diverse empirical domains.

stat.ME↗

arXiv2025

Understanding and Evaluating Engineering Creativity:Development and Validation of the Engineering Creativity Assessment Tool (ECAT)

Creativity is essential in engineering education, enabling students to develop innovative and practical solutions. However, assessing creativity remains challenging due to a lack of reliable, domain-specific tools. Traditional assessments like the Torrance Tests of Creative Thinking (TTCT) may not fully capture the complexity of engineering creativity. This study introduces and validates the Engineering Creativity Assessment Tool (ECAT), designed specifically for engineering contexts. ECAT was tested with 199 undergraduate students who completed a hands-on design task. Five trained raters evaluated the products using the ECAT rubric. Exploratory and confirmatory factor analyses supported a four-factor structure: fluency, originality, cognitive flexibility, and creative strengths. Reliability was high, convergent and discriminant validity were examined using TTCT scores, revealing moderate correlations that support ECATs domain specificity. ECAT offers a reliable, valid framework for assessing creativity in engineering education and provides actionable feedback to educators. Future work should examine its broader applicability across disciplines and instructional settings.

stat.OT↗

arXiv2026

Differential Privacy Meets Invariant Statistics: Some Conundrums in Quantifying Trade-Offs

This work was inspired by the question of whether data swapping, a popular form of statistical disclosure control used to protect many data products including three recent US Decennial Censuses, can satisfy differential privacy (DP). Given the existence of more than 200 formulations of DP (and counting), as a precondition to answering this question one must precisely specify what it actually means to be DP. Motivated by this observation, we first conduct a theoretical investigation into DP's fundamental essence, resulting in a five-building-block system explicating the who, where, what, how and how much aspects of DP. Instantiating this system in the context of the US Decennial Census, we then demonstrate the broad applicability and relevance of DP by comparing a swapping strategy like that used in 2010 with the TopDown Algorithm--the main DP method adopted in the 2020 Census. This chapter provides nontechnical summaries of these two pieces of work (developed elsewhere), as well as extended discussions on a number of issues they unearth that complicate the formulation and the navigation of the so-called privacy-utility trade-off: How can greater awareness of the five building blocks thwart privacy theatrics? How can invariants (statistics that are released as is, without any privacy protection) align with DP's philosophy of relative privacy? How do our results bridging traditional statistical disclosure control and DP allow a data custodian to reap the benefits of both these fields? And how can removing the implicit reliance on aleatoric uncertainty lead to new generalizations of DP? Our ultimate goal with these discussions is to deepen the theoretical basis, broaden the practical applicability, and reduce the misperception of DP--all without shaking its core foundations.

cs.CR↗

arXiv2026

Parental Imprints On Birth Weight: A Data-Driven Model For Neonatal Prediction In Low Resource Prenatal Care

Accurate fetal birth weight prediction is a cornerstone of prenatal care, yet traditional methods often rely on imaging technologies that remain inaccessible in resource-limited settings. This study presents a novel machine learning-based framework that circumvents these conventional dependencies, using a diverse set of physiological, environmental, and parental factors to refine birth weight estimation. A multi-stage feature selection pipeline filters the dataset into an optimized subset, demonstrating previously underexplored yet clinically relevant predictors of fetal growth. By integrating advanced regression architectures and ensemble learning strategies, the model captures non-linear relationships often overlooked by traditional approaches, offering a predictive solution that is both interpretable and scalable. Beyond predictive accuracy, this study addresses a question: whether birth weight can be reliably estimated without conventional diagnostic tools. The findings challenge entrenched methodologies by introducing an alternative pathway that enhances accessibility without compromising clinical utility. While limitations exist, the study lays the foundation for a new era in prenatal analytics, one where data-driven inference competes with, and potentially redefines, established medical assessments. By bridging computational intelligence with obstetric science, this research establishes a framework for equitable, technology-driven advancements in maternal-fetal healthcare.

stat.OT↗

arXiv2025

Spatiotemporal Assessment of Aircraft Noise Exposure Using Mobile Phone-Derived Population Estimates and High-Resolution Noise Measurements

Aircraft noise exposure has traditionally been assessed using static residential population data and long-term average noise metrics, often overlooking the dynamic nature of human mobility and temporal variations in operational conditions. This study proposes a data-driven framework that integrates high-resolution noise measurements from airport monitoring terminals with mobile phone-derived de facto population estimates to evaluate noise exposure with fine spatio-temporal resolution. We develop hourly noise exposure profiles and quantify the number of individuals affected across regions and time windows, using both absolute counts and inequality metrics such as Gini coefficients. This enables a nuanced examination of not only who is exposed, but when and where the burden is concentrated. At our case study airport, operational runway patterns resulted in recurring spatial shifts in noise exposure. By incorporating de facto population data, we demonstrate that identical noise operations can yield unequal impacts depending on the time and location of population presence, highlighting the importance of accounting for population dynamics in exposure assessment. Our approach offers a scalable basis for designing population-sensitive noise abatement strategies, contributing to more equitable and transparent aviation noise management.

stat.AP↗

arXiv2025

Analogy making as the basis of statistical inference

Standard statistical theory has arguably proved to be unsuitable as a basis for constructing a satisfactory completely general framework for performing statistical inference. For example, frequentist theory has never come close to providing such a general inferential framework, which is not only attributable to the question surrounding the soundness of this theory, but also to its focus on attempting to address the problem of how to perform statistical inference only in certain special cases. Also, theories of inference that are grounded in the idea of deducing sample-based inferences about populations of interest from a given set of universally acceptable axioms, e.g. many theories that aim to justify Bayesian inference and theories of imprecise probability, suffer from the difficulty of finding such axioms that are weak enough to be widely acceptable, but strong enough to lead to methods of inference that can be regarded as being efficient. These observations justify the need to look for an alternative means by which statistical inference may be performed, and in particular, to explore the one that is offered by analogy making. What is presented here goes down this path. To be clear, this is done in a way that does not simply endorse the common use of analogy making as a supplementary means of understanding how statistical methods work, but formally develops analogy making as the foundation of a general framework for performing statistical inference. In the latter part of the paper, the use of this framework is illustrated by applying some of the most important analogies contained within it to a relatively simple but arguably still unresolved problem of statistical inference, which naturally leads to an original way being put forward of addressing issues that relate to Bartlett's and Lindley's paradoxes.

stat.OT↗

arXiv2025

Local Polynomial Lp-norm Regression

The local least squares estimator for a regression curve cannot provide optimal results when non-Gaussian noise is present. Both theoretical and empirical evidence suggests that residuals often exhibit distributional properties different from those of a normal distribution, making it worthwhile to consider estimation based on other norms. It is suggested that $L_p$-norm estimators be used to minimize the residuals when these exhibit non-normal kurtosis. In this paper, we propose a local polynomial $L_p$-norm regression that replaces weighted least squares estimation with weighted $L_p$-norm estimation for fitting the polynomial locally. We also introduce a new method for estimating the parameter $p$ from the residuals, enhancing the adaptability of the approach. Through numerical and theoretical investigation, we demonstrate our method's superiority over local least squares in one-dimensional data and show promising outcomes for higher dimensions, specifically in 2D.

stat.ML↗

arXiv2025

On Bitcoin Price Prediction

In recent years, cryptocurrencies have attracted growing attention from both private investors and institutions. Among them, Bitcoin stands out for its impressive volatility and widespread influence. This paper explores the predictability of Bitcoin's price movements, drawing a parallel with traditional financial markets. We examine whether the cryptocurrency market operates under the efficient market hypothesis (EMH) or if inefficiencies still allow opportunities for arbitrage. Our methodology combines theoretical reviews, empirical analyses, machine learning approaches, and time series modeling to assess the extent to which Bitcoin's price can be predicted. We find that while, in general, the Bitcoin market tends toward efficiency, specific conditions, including information asymmetries and behavioral anomalies, occasionally create exploitable inefficiencies. However, these opportunities remain difficult to systematically identify and leverage. Our findings have implications for both investors and policymakers, particularly regarding the regulation of cryptocurrency brokers and derivatives markets.

q-fin.ST↗

arXiv2026

Conformal-DP: A Density-Aware Mechanism for Differential Privacy over Riemannian Manifolds via Conformal Transformation

Differential Privacy (DP) is being increasingly adopted for non-Euclidean data that lie on complex, high-dimensional manifolds. Existing DP mechanisms for manifold data consider geometric properties when calibrating privacy perturbations, but they largely fail to capture variations in data density within datasets, leading to biased perturbations and suboptimal privacy-utility trade-offs due to heterogeneous data distributions. In this paper, we propose a novel density-aware differential privacy mechanism on Riemannian manifolds, referred to as Conformal-DP, that leverages conformal transformations to calibrate perturbations based on local densities and to induce a density-balanced geometry. We prove that our mechanism satisfies $ε$-differential privacy on any complete Riemannian manifold under mild regularity assumptions. In addition, we derive a closed-form expected geodesic error bound that depends only on the underlying data density ratio and is independent of global curvature. Our empirical results on synthetic and real-world datasets demonstrate that the proposed Conformal-DP mechanism substantially improves the privacy-utility trade-off in heterogeneous data distribution settings, with worst-case performance comparable to state-of-the-art manifold DP mechanisms that assume uniformly distributed data.

cs.CR↗

arXiv2025

Rendering LaTeX in R

The xdvir package provides functions for rendering LaTeX fragments as labels, annotations, and data symbols in R plots. There are convenient high-level functions for rendering LaTeX fragments, including labels on ggplot2 plots, plus lower-level functions for more fine control over the separate authoring, typesetting, and rendering steps. There is support for making use of LaTeX packages, including TikZ graphics. The rendered LaTeX output is fully integrated with R graphics output in the sense that LaTeX output can be positioned and sized relative to R graphics output and vice versa.

stat.OT↗