A Class of Conjugate Priors Defined on the Unit Simplex

TL;DR

This paper introduces a new class of conjugate prior distributions on the unit simplex, extending the Dirichlet distribution to incorporate additional data-generating information for Bayesian models.

Contribution

It proposes a novel class of priors related to the Dirichlet distribution, enhancing Bayesian modeling capabilities with more flexible prior structures.

Findings

Potential for improved Bayesian inference with new priors

Examples demonstrate applicability to real data scenarios

Extensions broaden the scope of conjugate priors on the simplex

Abstract

Dirichlet distribution and Dirichlet process as its infinite dimensional generalization are primarily used conjugate prior of categorical and multinomial distributions in Bayesian statistics. Extensions have been proposed to broaden applications for different purposes. In this article, we explore a class of prior distributions closely related to Dirichlet distribution incorporating additional information on the data generating mechanism. Examples are given to show potential use of the models.