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A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…

Statistics Theory · Mathematics 2019-03-06 Michael Evans , Yang Guo

Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…

Statistics Theory · Mathematics 2023-11-15 Orestis Loukas , Ho Ryun Chung

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Statistics Theory · Mathematics 2025-11-25 Sayantan Banerjee , Ismaël Castillo , Subhashis Ghosal

We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility…

Artificial Intelligence · Computer Science 2022-02-17 Thierry Denoeux

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

Statistics Theory · Mathematics 2012-12-19 Natalia A. Bochkina , Peter J. Green

Divide-and-conquer methods use large-sample approximations to provide frequentist guarantees when each block of data is both small enough to facilitate efficient computation and large enough to support approximately valid inferences. When…

Methodology · Statistics 2025-04-01 Emily C. Hector , Leonardo Cella , Ryan Martin

Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…

Methodology · Statistics 2013-01-03 Jon Wellner , Tong Zhang

We describe inferactive data analysis, so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory (roughly speaking "model free")…

Statistics Theory · Mathematics 2017-07-24 Nan Bi , Jelena Markovic , Lucy Xia , Jonathan Taylor

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…

Other Statistics · Statistics 2011-06-23 Robert E. Kass

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Machine Learning · Computer Science 2025-01-03 Daniela de Albuquerque , John Pearson

This paper explores belief inference in credal networks using Dempster-Shafer theory. By building on previous work, we propose a novel framework for propagating uncertainty through a subclass of credal networks, namely chains. The proposed…

Artificial Intelligence · Computer Science 2025-07-11 Marco Sangalli , Thomas Krak , Cassio de Campos

Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…

Methodology · Statistics 2025-04-29 Xiahui Li , Fergus Chadwick , Ben Swallow

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

Machine Learning · Computer Science 2025-04-03 Caroline Tatsuoka , Minglei Yang , Dongbin Xiu , Guannan Zhang

While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…

Machine Learning · Statistics 2024-07-08 Maxime Cauchois , Suyash Gupta , Alnur Ali , John C. Duchi

In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and consequently it is important to understand the effects of misspecification on inferential procedures. When the hypothesized…

Methodology · Statistics 2025-09-01 Beomjo Park , Sivaraman Balakrishnan , Larry Wasserman

A theory of quantitative inference about the parameters of sampling distributions is constructed deductively by following very general rules, referred to as the Cox-Polya-Jaynes Desiderata. The inferences are made in terms of probability…

Statistics Theory · Mathematics 2017-08-23 Tomaz Podobnik , Tomi Zivko

Mathematical Theory of Evidence called also Dempster-Shafer Theory (DST) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its…

Artificial Intelligence · Computer Science 2017-07-14 Mieczysław A. Kłopotek

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…

Statistics Theory · Mathematics 2013-01-23 Ali Kinkhabwala

It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…

Computation · Statistics 2018-05-22 Randy C. S. Lai , J. Hannig , Thomas C. M. Lee

This paper serves as a literature review of methodology concerning the (modern) causal inference methods to address the causal estimand with observational/survey data that have been or will be used in social science research. Mainly, this…

Econometrics · Economics 2024-08-02 Guanghui Pan