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We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

Machine Learning · Statistics 2022-09-07 Joel Janek Dabrowski , Daniel Edward Pagendam

Given data from a Poisson point process with intensity $(x,y) \mapsto n \mathbf{1}(f(x)\leq y),$ frequentist properties for the Bayesian reconstruction of the support boundary function $f$ are derived. We mainly study compound Poisson…

Statistics Theory · Mathematics 2018-09-13 Markus Reiss , Johannes Schmidt-Hieber

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

Methodology · Statistics 2020-05-13 Ilja Klebanov , Alexander Sikorski , Christof Schütte , Susanna Röblitz

In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of…

Statistics Theory · Mathematics 2015-12-04 Daniel Williamson , Michael Goldstein

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the…

Methodology · Statistics 2025-10-14 Carlos García Meixide , David Ríos Insua

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…

Methodology · Statistics 2022-07-27 F. Llorente , L. Martino , E. Curbelo , J. Lopez-Santiago , D. Delgado

This paper studies quasi Bayesian estimation and uncertainty quantification for an unknown function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors.…

Econometrics · Economics 2023-11-08 Sid Kankanala

The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this over-confidence are unknown. In general, the performance of Bayesian…

Statistics Theory · Mathematics 2018-10-15 Ziheng Yang , Tianqi Zhu

Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…

Machine Learning · Statistics 2025-05-07 Etienne Gauthier , Francis Bach , Michael I. Jordan

Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…

Artificial Intelligence · Computer Science 2013-04-15 Alf C. Zimmer

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…

Statistics Theory · Mathematics 2007-06-13 B. Clarke , Ao Yuan

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Methodology · Statistics 2012-05-02 David R. Bickel

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Statistics Theory · Mathematics 2020-02-04 Vladimir Spokoiny

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Machine Learning · Statistics 2019-09-12 Tomasz Kuśmierczyk , Joseph Sakaya , Arto Klami

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…

Methodology · Statistics 2019-09-13 Spencer Woody , Novin Ghaffari , Lauren Hund

We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…

Methodology · Statistics 2022-05-13 David T. Frazier , Ruben Loaiza-Maya , Gael M. Martin , Bonsoo Koo

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

Methodology · Statistics 2009-01-27 K. Triantafyllopoulos , P. J. Harrison

Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…

Methodology · Statistics 2015-07-30 Elías Moreno , Javier Girón , George Casella

Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper,…

Statistics Theory · Mathematics 2018-02-23 Robert Bassett , Julio Deride

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably…

Statistics Theory · Mathematics 2007-06-13 James O. Berger , William Strawderman , Dejun Tang