Work

Nonparametric Full Bayesian Significance Testing for Bayesian Histograms

Year: 2025

Type: conference-paper

Abstract: In this article, we present an extension of the Full Bayesian Significance Test (FBST) for nonparametric settings, termed NP-FBST, which is constructed using the limit of finite dimension histograms. The test statistics for NP-FBST are based on a plug-in estimate of the cross-entropy between the null hypothesis and a histogram. This method shares similarities with Kullback–Leibler and entropy-based goodness-of-fit tests, but it can be applied to a broader range of hypotheses and is generally less computationally intensive. We demonstrate that when the number of histogram bins increases slowly with the sample size, the NP-FBST is consistent for Lipschitz continuous data-generating densities. Additionally, we propose an algorithm to optimize the NP-FBST. Through simulations, we compare the performance of the NP-FBST to traditional methods for testing uniformity. Our results indicate that the NP-FBST is competitive in terms of power, even surpassing the most powerful likelihood-ratio-based procedures for very small sample sizes.

Source: International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt)

DOI: 10.3390/psf2025012011

Authors: Fernando Corrêa, Julio Michael Stern, Rafael Bassi Stern

Institution: Universidade de São Paulo

Language: English

Topic: Statistical Methods and Bayesian Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Awards: G2823776494, G3519237112