On posterior contraction of parameters and interpretability in Bayesian\n mixture modeling

2019/01/15 by Aritra Guha, Guha, Aritra, Nhat Ho +3 · 6 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1901.05078

openalex publication_date 2019/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study posterior contraction behaviors for parameters of interest in the\ncontext of Bayesian mixture modeling, where the number of mixing components is\nunknown while the model itself may or may not be correctly specified. Two\nrepresentative types of prior specification will be considered: one requires\nexplicitly a prior distribution on the number of mixture components, while the\nother places a nonparametric prior on the space of mixing distributions. The\nformer is shown to yield an optimal rate of posterior contraction on the model\nparameters under minimal conditions, while the latter can be utilized to\nconsistently recover the unknown number of mixture components, with the help of\na fast probabilistic post-processing procedure. We then turn the study of these\nBayesian procedures to the realistic settings of model misspecification. It\nwill be shown that the modeling choice of kernel density functions plays\nperhaps the most impactful roles in determining the posterior contraction rates\nin the misspecified situations. Drawing on concrete posterior contraction rates\nestablished in this paper we wish to highlight some aspects about the\ninteresting tradeoffs between model expressiveness and interpretability that a\nstatistical modeler must negotiate in the rich world of mixture modeling.\n

Cited by

• Considering parallel tempering and comparing post-treatment procedures in Bayesian Profile Regression Models for a survival outcome and correlated exposures
• Learning Heterogeneous Ordinal Graphical Models via Bayesian Nonparametric Clustering
• Panel data models with randomly generated groups
• Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps
• A fast non-reversible sampler for Bayesian finite mixture models
• Understanding uncertainty in Bayesian cluster analysis

Related

• A Bayesian approach to learning mixtures of nonparametric components
• Consistency of mixture models with a prior on the number of components
• Anchored Bayesian Gaussian Mixture Models
• Fast sampling and model selection for Bayesian mixture models
• On choosing mixture components via non-local priors