Order Selection of the Finite Mixture Models

Abstract

The order selection problem, in contrast to determining whether a lower-ordered finite mixture model should be rejected in favor of a higher-ordered model, seeks to answer the question of what constitutes the most appropriate order for the finite mixture model. The challenge here lies in the fact that there are as many criteria for ”most suitable” as there are statisticians, making it a far more diverse problem than a simple hypothesis test. Moreover, each of these criteria often cannot be directly evaluated but requires approximations using complex asymptotic tools. The already intricate nature of finite mixture models further compounds this challenge. In Chap. 16, we offer a brief overview of several order selection procedures for finite mixture models. These include the transplanted Akaike Information Criterion (AIC), Bayes Information Criterion (BIC), as well as somewhat tailored Widely Applicable Bayesian Information Criterion (WBIC) and Singular Bayesian Information Criterion (sBIC), in addition to regularization-based techniques. This chapter serves as a limited introduction to these various methods without endorsing any particular approach.