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Flexible Bayesian Multiple Comparison Adjustment Using Dirichlet Process and Beta-Binomial Model Priors

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Bibliographic Details
Title: Flexible Bayesian Multiple Comparison Adjustment Using Dirichlet Process and Beta-Binomial Model Priors
Authors: Don van den Bergh, Fabian Dablander
Source: The American Statistician. :1-23
Publication Status: Preprint
Publisher Information: Informa UK Limited, 2025.
Publication Year: 2025
Subject Terms: Methodology (stat.ME), FOS: Computer and information sciences, 05 social sciences, FOS: Mathematics, Mathematics - Statistics Theory, 0501 psychology and cognitive sciences, Statistics Theory (math.ST), 0101 mathematics, 62F15 (Primary) 62P15 (Secondary), 01 natural sciences, Statistics - Methodology
Description: Researchers frequently wish to assess the equality or inequality of groups, but this poses the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can be uniquely represented as partitions of groups, where any number of groups are equal if they are in the same subset of the partition. In a Bayesian framework, one can adjust for multiple comparisons by constructing a suitable prior distribution over all possible partitions. Inspired by work on variable selection in regression, we propose a class of flexible beta-binomial priors for multiple comparison adjustment. We compare this prior setup to the Dirichlet process prior suggested by Gopalan and Berry (1998) and multiple comparison adjustment methods that do not specify a prior over partitions directly. Our approach not only allows researchers to assess pairwise equality constraints but simultaneously all possible equalities among all groups. Since the space of possible partitions grows rapidly -- for ten groups, there are already 115,975 possible partitions -- we use a stochastic search algorithm to efficiently explore the space. Our method is implemented in the Julia package EqualitySampler, and we illustrate it on examples related to the comparison of means, standard deviations, and proportions.
31 pages, 12 figures, and 2 tables
Document Type: Article
Other literature type
Language: English
ISSN: 1537-2731
0003-1305
DOI: 10.1080/00031305.2025.2561146
DOI: 10.48550/arxiv.2208.07086
DOI: 10.6084/m9.figshare.30142509.v1
DOI: 10.6084/m9.figshare.30142509
Access URL: http://arxiv.org/abs/2208.07086
Rights: CC BY
CC BY SA
Accession Number: edsair.doi.dedup.....7bc52072c57896a2c21520e516f6ae99
Database: OpenAIRE
Description
Abstract:Researchers frequently wish to assess the equality or inequality of groups, but this poses the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can be uniquely represented as partitions of groups, where any number of groups are equal if they are in the same subset of the partition. In a Bayesian framework, one can adjust for multiple comparisons by constructing a suitable prior distribution over all possible partitions. Inspired by work on variable selection in regression, we propose a class of flexible beta-binomial priors for multiple comparison adjustment. We compare this prior setup to the Dirichlet process prior suggested by Gopalan and Berry (1998) and multiple comparison adjustment methods that do not specify a prior over partitions directly. Our approach not only allows researchers to assess pairwise equality constraints but simultaneously all possible equalities among all groups. Since the space of possible partitions grows rapidly -- for ten groups, there are already 115,975 possible partitions -- we use a stochastic search algorithm to efficiently explore the space. Our method is implemented in the Julia package EqualitySampler, and we illustrate it on examples related to the comparison of means, standard deviations, and proportions.<br />31 pages, 12 figures, and 2 tables
ISSN:15372731
00031305
DOI:10.1080/00031305.2025.2561146