On posterior contraction of parameters and interpretability in Bayesian mixture modeling

by   Aritra Guha, et al.

We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two representative types of prior specification will be considered: one requires explicitly a prior distribution on the number of mixture components, while the other places a nonparametric prior on the space of mixing distributions. The former is shown to yield an optimal rate of posterior contraction on the model parameters under minimal conditions, while the latter can be utilized to consistently recover the unknown number of mixture components, with the help of a fast probabilistic post-processing procedure. We then turn the study of these Bayesian procedures to the realistic settings of model misspecification. It will be shown that the modeling choice of kernel density functions plays perhaps the most impactful roles in determining the posterior contraction rates in the misspecified situations. Drawing on concrete posterior contraction rates established in this paper we wish to highlight some aspects about the interesting tradeoffs between model expressiveness and interpretability that a statistical modeler must negotiate in the rich world of mixture modeling.


Optimal Bayesian estimation of Gaussian mixtures with growing number of components

We study posterior concentration properties of Bayesian procedures for e...

Bayesian Inference for k-Monotone Densities with Applications to Multiple Testing

Shape restriction, like monotonicity or convexity, imposed on a function...

A Divide and Conquer Algorithm of Bayesian Density Estimation

Data sets for statistical analysis become extremely large even with some...

Posterior Consistency in the Binomial (n,p) Model with Unknown n and p: A Numerical Study

Estimating the parameters from k independent Bin(n,p) random variables, ...

A one-dimensional morphoelastic model for burn injuries: sensitivity analysis and a feasibility study

We consider a one-dimensional morphoelastic model describing post-burn s...

Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes

By expressing prior distributions as general stochastic processes, nonpa...

On Excess Mass Behavior in Gaussian Mixture Models with Orlicz-Wasserstein Distances

Dirichlet Process mixture models (DPMM) in combination with Gaussian ker...

Please sign up or login with your details

Forgot password? Click here to reset