Approximate Bayesian Computation for Finite Mixture Models

TL;DR

This paper introduces an extension of the ABC-PMC algorithm tailored for finite mixture models, addressing challenges like multimodality and label switching, and demonstrates its effectiveness through simulations and real data.

Contribution

The paper develops a novel ABC-PMC framework specifically designed for finite mixture models, tackling key inference challenges and providing practical implementation guidance.

Findings

Effective in handling multimodal likelihoods

Addresses label switching in mixture models

Performs well on simulated and real galaxy data

Abstract

Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose extensions of the Approximate Bayesian Computation-Population Monte Carlo (ABC-PMC) algorithm as an alternative framework for inference on finite mixture models. There are several decisions to make when implementing an ABC-PMC algorithm for finite mixture models, including the selection of the kernels used for moving the particles through the iterations, how to address the label switching problem, and the choice of informative summary statistics. Examples are presented to demonstrate the performance of the proposed ABC-PMC algorithm for mixture modeling. The performance of the proposed method is evaluated in a simulation study and for the popular recessional velocity galaxy data.