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The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Methodology · Statistics 2015-06-22 Jeffrey W. Miller , David B. Dunson

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Methodology · Statistics 2024-07-02 Isadora Antoniano-Villalobos , Emanuele Borgonovo , Xuefei Lu

Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…

Mathematical Physics · Physics 2009-11-10 Adel Mohammadpour , Ali Mohammad-Djafari

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…

Methodology · Statistics 2024-10-30 Jesus Enrique Achire Quispe , Eduardo Ramos , Pedro Luiz Ramos

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

Machine Learning · Statistics 2025-01-22 Katharine Fisher , Youssef Marzouk

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…

Artificial Intelligence · Computer Science 2013-04-11 Thomas Slack

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…

Computation · Statistics 2012-11-20 Nicolas Chopin , Judith Rousseau , Brunero Liseo

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…

Methodology · Statistics 2025-05-06 Martin Bladt , Jorge González Cázares

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Data Analysis, Statistics and Probability · Physics 2013-01-31 Andreas Raue , Clemens Kreutz , Fabian Joachim Theis , Jens Timmer

This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…

Statistics Theory · Mathematics 2014-11-03 Lucien Birgé

Piecewise constant priors are routinely used in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, large sample properties of this Bayesian method are not yet well understood. This work provides a…

Statistics Theory · Mathematics 2023-06-16 Bo Y. -C. Ning , Ismaël Castillo

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

How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…

Data Analysis, Statistics and Probability · Physics 2018-10-24 Wei-Chia Chen , Ammar Tareen , Justin B. Kinney

Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…

Statistics Theory · Mathematics 2022-09-27 Jasper Marijn Everink , Yiqiu Dong , Martin Skovgaard Andersen

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

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

Methodology · Statistics 2020-03-18 Marcelo Hartmann , Georgi Agiashvili , Paul Bürkner , Arto Klami

Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…

Statistics Theory · Mathematics 2020-03-10 Oscar Oelrich , Shutong Ding , Måns Magnusson , Aki Vehtari , Mattias Villani

We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs…

Computer Science and Game Theory · Computer Science 2022-02-07 Itai Arieli , Yakov Babichenko

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Statistics Theory · Mathematics 2015-10-15 Ismaël Castillo , Johannes Schmidt-Hieber , Aad van der Vaart

Differential privacy formalises privacy-preserving mechanisms that provide access to a database. We pose the question of whether Bayesian inference itself can be used directly to provide private access to data, with no modification. The…