🤖 AI Summary
This work addresses the challenge of Bayesian inference in non-conjugate distance-dependent Chinese Restaurant Processes (ddCRP), where the lack of conjugacy between cluster parameters and the likelihood leads to a parameter space of varying dimensionality. To tackle this, the authors develop a reversible-jump Markov chain Monte Carlo (RJMCMC) framework that incorporates multiple birth-death move strategies based on prior matching, independence, and moment matching with respect to the data. A posterior resampling mechanism is introduced to enhance the acceptance rate of fixed-dimensional moves. By combining moment-matching proposal distributions with resampling techniques, the proposed method accommodates both discrete and continuous observation models. Experiments on synthetic data and the Old Faithful geyser eruption dataset demonstrate that moment-matching proposals substantially outperform conventional prior-based proposals, yielding efficient and accurate inference for non-conjugate ddCRP models.
📝 Abstract
The distance dependent Chinese Restaurant Process (ddCRP) provides a flexible prior distribution for clustering observations, incorporating covariate information through pairwise distances and accommodating a rich variety of cluster structures. When cluster parameters are conjugate to the likelihood, Bayesian inference is straightforward. In the non-conjugate setting, however, inference becomes substantially more challenging due to the trans-dimensional parameter spaces that arise as cluster assignments change. We develop a reversible jump Markov chain Monte Carlo (RJMCMC) framework to address this challenge, targeting the dimension-changing nature of cluster parameter vectors when observation assignments are updated. We introduce and compare several proposal strategies for birth and death moves, including prior-based, independence, and data-driven moment-matching proposals that target regions of high posterior density. For fixed-dimensional moves, we propose a posterior resampling strategy that improves acceptance rates while maintaining computational efficiency. Through a simulation study and an application to Old Faithful eruption durations, we demonstrate moment-matched proposals offer a principled, data-driven alternative to prior-based proposals. The resulting methodology provides a general RJMCMC framework for ddCRP models with non-conjugate likelihoods, demonstrated here on both discrete and continuous observation models.