Chained Markov melding using divide and conquer sequential Monte Carlo

TL;DR

This paper introduces a divide-and-conquer sequential Monte Carlo method for efficient Bayesian inference in chained Markov models with multiple submodels, overcoming challenges of existing MCMC approaches.

Contribution

It proposes a novel multi-stage sampler that leverages the tree structure of chained Markov melding, enabling flexible and efficient inference for complex joint models.

Findings

Successfully applied to a toy example with 11 submodels

Demonstrated on an ecological population model combining multiple datasets

Avoids direct sampling from the full complex model

Abstract

Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding. However, when adjacent submodels share common quantities, as in chained Markov melding, posterior inference can be challenging for existing MCMC-based approaches. In this paper, we propose a new multi-stage sampler for chained Markov models involving an arbitrary number of submodels. The proposed sampler adopts a divide-and-conquer sequential Monte Carlo approach for the tree-structured model that fits naturally with the structure of chained Markov melding. The resulting multi-stage sampler provides a flexible alternative for sampling from complex joint models, as its separate sampling scheme for different submodels avoids the need for directly sampling from the full model. We demonstrate applications of the sampler through two examples. The first is a toy example involving 11 submodels of various types. The second example considers an ecologically integrated population model that combines multiple datasets to estimate immigration and reproduction rates.