An adaptive truncation method for inference in Bayesian nonparametric models

TL;DR

This paper introduces an adaptive truncation approach for Bayesian nonparametric inference that dynamically determines the truncation level to control approximation errors, using a combination of MCMC and sequential Monte Carlo methods.

Contribution

It presents a novel adaptive truncation method that automatically adjusts the truncation level in Bayesian nonparametric models, improving inference accuracy.

Findings

Effective in infinite mixture models with stick-breaking priors

Applicable to semiparametric linear mixed models

Demonstrates improved posterior approximation control

Abstract

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be developed for different classes of prior or different models. Alternatively, the infinite-dimensional prior can be truncated and standard Markov chain Monte Carlo methods used for inference. However, the error in approximating the infinite-dimensional posterior can be hard to control for many models. This paper describes an adaptive truncation method which allows the level of the truncation to be decided by the algorithm and so can avoid large errors in approximating the posterior. A sequence of truncated priors is constructed which are sampled using Markov chain Monte Carlo methods embedded in a sequential Monte Carlo algorithm. Implementational details for infinite mixture models with stick-breaking priors and normalized random measures with independent increments priors are discussed. The methodology is illustrated on infinite mixture models, a semiparametric linear mixed model and a nonparametric time series model.