Chained Markov melding using divide and conquer sequential Monte Carlo

2026-05-21

AI Summary

This work addresses the challenge of posterior inference in chained Markov fusion models, where shared variables between adjacent submodels complicate computation. To overcome this, the authors propose a multi-stage sequential Monte Carlo (SMC) sampler based on a divide-and-conquer strategy. This approach introduces divide-and-conquer SMC into the chained Markov fusion framework for the first time, decomposing the model using a tree structure to enable flexible composition of an arbitrary number of heterogeneous submodels and efficient Bayesian inference. Experimental results demonstrate that the method accurately estimates key parameters—such as immigration and reproduction rates—in both a synthetic example comprising 11 submodels and an ecological integrated population model, significantly improving inference efficiency and scalability.

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.

Problem

• chained Markov melding
• posterior inference
• Bayesian model
• submodels
• shared quantities

Innovation

• chained Markov melding
• sequential Monte Carlo
• divide and conquer
• multi-stage sampler
• Bayesian integration