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The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

Methodology · Statistics 2026-05-19 Mike Crowhurst

In many scientific and technological contexts we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal…

Algebraic Topology · Mathematics 2021-11-04 Sean T. Vittadello , Michael P. H. Stumpf

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Machine Learning · Computer Science 2013-02-21 George H. John , Pat Langley

Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…

Information Theory · Computer Science 2025-07-08 Hippolyte Charvin , Nicola Catenacci Volpi , Daniel Polani

A vast array of transformative technologies developed over the past decade has enabled measurement and perturbation at ever increasing scale, yet our understanding of many systems remains limited by experimental capacity. Overcoming this…

Quantitative Methods · Quantitative Biology 2020-12-25 Brian Cleary , Aviv Regev

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…

Current pooling rules for multiply imputed data assume infinite populations. In some situations this assumption is not feasible as every unit in the population has been observed, potentially leading to over-covered population estimates. We…

Statistics Theory · Mathematics 2014-10-01 Gerko Vink , Stef van Buuren

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

Other Statistics · Statistics 2025-02-11 Paul W. Vos

Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…

Machine Learning · Statistics 2022-06-16 Daniel Ting

Deep neural two-sample tests have recently shown strong power for detecting distributional differences between groups, yet their black-box nature limits interpretability and practical adoption in biomedical analysis. Moreover, most existing…

Computer Vision and Pattern Recognition · Computer Science 2026-02-06 Masoumeh Javanbakhat , Piotr Komorowski , Dilyara Bareeva , Wei-Chang Lai , Wojciech Samek , Christoph Lippert

Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it…

Machine Learning · Statistics 2016-05-10 Giulio Caravagna , Luca Bortolussi , Guido Sanguinetti

This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with…

Methodology · Statistics 2016-06-17 Rahul Mukerjee , Tirthankar Dasgupta , Donald B. Rubin

We consider a discrete model that describes a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize this model by adding…

Probability · Mathematics 2007-05-23 Nicolas Fournier , Sylvie Meleard

Randomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to…

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…

Machine Learning · Computer Science 2025-07-24 Jacqueline Maasch , Willie Neiswanger , Stefano Ermon , Volodymyr Kuleshov

This paper provides a design-based framework for variance (bound) estimation in experimental analysis. Results are applicable to virtually any combination of experimental design, linear estimator (e.g., difference-in-means, OLS, WLS) and…

Methodology · Statistics 2021-09-21 Joel A. Middleton

While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability…

Artificial Intelligence · Computer Science 2020-06-18 Guangyi Zhang , Aristides Gionis

A new strategy is introduced for estimating population size and networked population characteristics. Sample selection is based on a multi-wave snowball sampling design. A generalized stochastic block model is posited for the population's…

Methodology · Statistics 2019-07-30 Kyle Vincent , Steve Thompson

The cross-classified sampling design consists in drawing samples from a two-dimension population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample…

Statistics Theory · Mathematics 2015-11-23 Hélène Juillard , Guillaume Chauvet , Anne Ruiz-Gazen

We consider fair network topology inference from nodal observations. Real-world networks often exhibit biased connections based on sensitive nodal attributes. Hence, different subpopulations of nodes may not share or receive information…

Signal Processing · Electrical Eng. & Systems 2024-03-26 Madeline Navarro , Samuel Rey , Andrei Buciulea , Antonio G. Marques , Santiago Segarra