The Jackknife-Like Method for Assessing Uncertainty of Point Estimates for Bayesian Estimation in a Finite Gaussian Mixture Model

Kuntalee Chaisee

Abstract

In this paper, we follow the idea of using an invariant loss function in a decision theoretic approach for point estimation in Bayesian mixture models presented in [1]. Although using this approach the so-called label switching is no longer a problem, it is diffcult to assess the uncertainty. We propose a simple and accessible way for assessing uncertainty using the leaving-out idea from the jackknife method to compute the Bayes estimates called jackknife-Bayes estimates, then use them to visualize the uncertainty of Bayesian point estimates. This paper is primarily related to simulation-based point estimation using Markov Chain Monte Carlo (MCMC) samples; hence the MCMC methods, in particular Gibbs sampling and Metropolis Hastings method are used to approximate the posterior mixture models. We also present the use of importance sampling in reduced posterior mixture distribution corresponding to the leaving-out observation.