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The celebrated Bernstein von-Mises theorem ensures that credible regions from Bayesian posterior are well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal…

Methodology · Statistics 2021-09-17 Rong Tang , Yun Yang

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…

Methodology · Statistics 2026-01-21 Yu Luo , David A. Stephens , Daniel J. Graham , Emma J. McCoy

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Methodology · Statistics 2026-04-03 Lachlan Astfalck , Deborshee Sen , Sayan Patra , Edward Cripps , David Dunson

This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…

Statistics Theory · Mathematics 2023-11-21 Natalia Bochkina

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…

Statistics Theory · Mathematics 2026-03-02 Edwin Fong , Andrew Yiu

Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…

Statistics Theory · Mathematics 2011-02-04 Guang Cheng , Jianhua Z. Huang

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Statistics Theory · Mathematics 2021-04-16 François Monard , Richard Nickl , Gabriel P. Paternain

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice.…

This paper proposes a valid bootstrap-based distributional approximation for M-estimators exhibiting a Chernoff (1964)-type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is inconsistent. The method…

Statistics Theory · Mathematics 2020-06-01 Matias D. Cattaneo , Michael Jansson , Kenichi Nagasawa

The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…

Statistics Theory · Mathematics 2025-04-01 Clément Dombry , Simone A. Padoan , Stefano Rizzelli

Modular Bayesian methods perform inference in models that are specified through a collection of coupled sub-models, known as modules. These modules often arise from modelling different data sources or from combining domain knowledge from…

Methodology · Statistics 2024-11-26 David T. Frazier , David J. Nott

The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…

Econometrics · Economics 2018-09-12 Joel L. Horowitz

High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…

Statistics Theory · Mathematics 2025-07-09 Yiqi Tang , Ryan Martin

This paper develops distribution theory and bootstrap-based inference methods for a broad class of convex pairwise difference estimators. These estimators minimize a kernel-weighted convex-in-parameter function over observation pairs with…

Econometrics · Economics 2026-05-29 Matias D. Cattaneo , Michael Jansson , Kenichi Nagasawa

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Statistics Theory · Mathematics 2010-01-13 Yuan Liao , Wenxin Jiang

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…

Numerical Analysis · Mathematics 2019-09-04 Chen Zhang , Simon Arridge , Bangti Jin

In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…

Computation · Statistics 2013-07-11 Yuao Hu , Kaifeng Zhao , Heng Lian

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

Methodology · Statistics 2018-05-09 David T. Frazier , Gael M. Martin , Christian P. Robert , Judith Rousseau

This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…

Econometrics · Economics 2023-08-15 Kenichi Shimizu

The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…

Statistics Theory · Mathematics 2020-06-02 Vladimir Spokoiny , Maxim Panov