Deriving Proper Uniform Priors for Regression Coefficients, Part II

TL;DR

This paper develops a proper uniform prior for regression coefficients in Bayesian model selection, enabling accurate computation of model evidence and posterior probabilities, thus improving the reliability of Bayesian inference in regression analysis.

Contribution

It introduces a new proper uniform prior for regression coefficients and derives model evidence values, facilitating better Bayesian model comparison.

Findings

Derived a proper uniform prior for regression coefficients.

Provided a method to compute model evidence values.

Enabled calculation of posterior model probabilities.

Abstract

It is a relatively well-known fact that in problems of Bayesian model selection improper priors should, in general, be avoided. In this paper we derive a proper and parsimonious uniform prior for regression coefficients. We then use this prior to derive the corresponding evidence values of the regression models under consideration. By way of these evidence values one may proceed to compute the posterior probabilities of the competing regression models.