Sponsor
Womack was partially supported by NIH award 5R01DC018813-04. Taylor-Rodríguez was partially supported by NSF RTG DMS award 2136228, NIH award 5R01DC018813-04, and by Portland State University’s FDG and Sabbatical programs.
Published In
Bayesian Analysis
Document Type
Article
Publication Date
2025
Subjects
Regression analysis, Bayesian methods, Bayesian statistical decision theory
Abstract
This paper introduces a general and principled construction of model space priors with a focus on regression problems. The proposed formulation regards each model as a “local” null hypothesis whose alternatives are the set of models that nest it. Assuming constant ratio of prior probabilities for any “local” null and its alternatives provides a natural isomorphism of model spaces (like a matryoshka doll), constituting an intuitive way to correct for multiplicity in Bayesian model selection and averaging problems. This isomorphism yields the Poisson distribution as the unique limiting distribution over model dimension under mild assumptions. We compare this model space prior theoretically and in simulations to widely adopted Beta-Binomial constructions. We show that the proposed prior yields a “just-right” multiplicity correction that induces a desirable complexity penalization profile.
Locate the Document
DOI
10.1214/25-BA1580
Persistent Identifier
https://archives.pdx.edu/ds/psu/44428
Citation Details
Andrew Womack. Daniel Taylor-Rodríguez. Claudio Fuentes. "The Matryoshka Doll Prior – Principled Multiplicity Correction in Bayesian Model Comparison." Bayesian Anal. Advance Publication 1 - 25, 2025. https://doi.org/10.1214/25-BA1580