Related papers: Comparison of Bayesian and Frequentist Multiplicit…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…

External controls from historical trials or observational data can augment randomized controlled trials when large-scale randomization is impractical or unethical, such as in drug evaluation for rare diseases. However, non-randomized…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or…

Mutual information is a well-known tool to measure the mutual dependence between variables. In this paper, a Bayesian nonparametric estimation of mutual information is established by means of the Dirichlet process and the $k$-nearest…

Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian…

Given the well-known and fundamental problems with hypothesis testing via classical (point-form) significance tests, there has been a general move to alternative approaches, often focused on the Bayesian t-test. We show that the Bayesian…

Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and…

We consider Bayesian multiple hypothesis problem with independent and identically distributed observations. The classical, Sanov's theorem-based, analysis of the error probability allows one to characterize the best achievable error…

In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…

Interim analyses are vital in clinical trials for early decision-making. While frequentist implications are well-established, the consequences of repeated Bayesian interim monitoring for efficacy, specifically regarding multiplicity, remain…

Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence…

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and…

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…

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…

False discovery rate (FDR) has been widely used as an error measure in large scale multiple testing problems, but most research in the area has been focused on procedures for controlling the FDR based on independent test statistics or the…

We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection…