Approximate Bayesian computation for finite mixture models

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 modelling. The performance of the proposed method is evaluated in a simulation study and for the popular recessional velocity galaxy data.

On Finite and Non-Finite Bayesian Mixture Models

“…This makes it feasible for emergence of any inferential probabilistic prior with its corresponding likelihood to yield closed form solution and limiting distribution for the embedded parameters. Contrary to the adoption of priors' principles, [7] proposed Approximate Bayesian Computation-Population Monte Carlo (ABC-PMC) algorithm as an alternative technique for finite mixture model inferential. [7] adopted a kernel function as a substitute for prior distribution and explicitly highlighted how the problem of label switching can be solved with the use of the adopted kernel.…”

“…Contrary to the adoption of priors' principles, [7] proposed Approximate Bayesian Computation-Population Monte Carlo (ABC-PMC) algorithm as an alternative technique for finite mixture model inferential. [7] adopted a kernel function as a substitute for prior distribution and explicitly highlighted how the problem of label switching can be solved with the use of the adopted kernel. In extension, [8] adopted Bayes factor to find required number of K-components that will be associated to a finite mixture model.…”

The Bibliometric Analysis on Finite Mixture Model

“…The rapid development of computer technology provided statisticians with the idea of exploring probabilistic models for analyzing and handling complex properties of massive data. The mixture model is ubiquitous in statistics as it has been proven to be an excellent framework for modeling clustered data (Simola et al, 2021). Subsequently, a considerable shift from a single distribution to a mixture distribution occurred due to increased methodological complications (Makov, 2001).…”