A new test for the presence of a normal mixture distribution based on the posterior Bayes factor

Abstract

We present a new test for the presence of a normal mixture distribution, based on the posterior Bayes factor of Aitkin (1991). The new test has slightly lower power than the likelihood ratio test. It does not require the computation of the MLEs of the parameters or a search for multiple maxima, but requires computations based on 'classification likelihood' assignments of observations to mixture components.

Bayesian selection of dependence structures for Markovian processes

“…To avoid such intractable quantities, we use the Monte Carlo approximations of the Intrinsic Bayes Factor (Berger and Pericchi, 1996), which is based on averaging over posterior distributions, that tend to be highly concentrated within a small set of context trees for VLMC models, and have been used recently in many different fields with the same purpose, such as Cabras et al (2015), Charitidou et al (2018) and Villa and Walker (2021). Alternatives to Bayes Factors based on using posterior distributions instead of the prior distribution in integrations have been evolving over the past decades, the classical method using this strategy is the Posterior Bayes Factor (Aitkin, 1991), with applications in a variety of models such as Aitkin (1993) and Aitkin et al (1996).…”