Martingale Posterior Inference for Finite Mixture Models and Clustering

Martingale posterior inference is employed to quantify uncertainty for a finite mixture model with an unknown number of components. New ideas for Bayesian analysis, particularly focusing on martingale posterior distributions, are applied to focus on clustering. The fundamental concept involves constructing appropriate martingales for the unknown parameters. A key outcome of this approach is the ability to conduct posterior analysis of clusters while circumventing the label-switching problem. This methodology is further extended to finite populations, where the mixture is used to impute the missing part of the population and perform inference for the parameter of interest. The proposed methodology is demonstrated through the analysis of four real datasets. Supplementary materials for this article are available online.