Bayesian Inference for Non-Conjugate Distance Dependent Chinese Restaurant Process Models
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| Format: | Preprint |
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2026
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| author | Marsh, Joseph Kypraios, Theodore Seymour, Rowland G. |
| author_facet | Marsh, Joseph Kypraios, Theodore Seymour, Rowland G. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15847 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian Inference for Non-Conjugate Distance Dependent Chinese Restaurant Process Models Marsh, Joseph Kypraios, Theodore Seymour, Rowland G. Methodology Computation 62H30 (Primary), 65C05 (Secondary), 62F15 (Secondary) G.3; I.5.3 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. |
| title | Bayesian Inference for Non-Conjugate Distance Dependent Chinese Restaurant Process Models |
| topic | Methodology Computation 62H30 (Primary), 65C05 (Secondary), 62F15 (Secondary) G.3; I.5.3 |
| url | https://arxiv.org/abs/2605.15847 |