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In this paper, we address technical difficulties that arise when applyingMarkov chain Monte Carlo (MCMC) to hierarchical models designed to performclustering in the space of latent parameters of subject-wise generative models.Specifically, we focus on the case where the subject-wise generative model is adynamic causal model (DCM) for fMRI and clusters are defined in terms ofeffective brain connectivity. While an attractive approach for detectingmechanistically interpretable subgroups in heterogeneous populations, invertingsuch a hierarchical model represents a particularly challenging case, since DCMis often characterized by high posterior correlations between its parameters.In this context, standard MCMC schemes exhibit poor performance and extremelyslow convergence. In this paper, we investigate the properties of hierarchicalclustering which lead to the observed failure of standard MCMC schemes andpropose a solution designed to improve convergence but preserve computationalcomplexity. Specifically, we introduce a class of proposal distributions whichaims to capture the interdependencies between the parameters of the clusteringand subject-wise generative models and helps to reduce random walk behaviour ofthe MCMC scheme. Critically, these proposal distributions only introduce asingle hyperparameter that needs to be tuned to achieve good performance. Forvalidation, we apply our proposed solution to synthetic and real-world datasetsand also compare it, in terms of computational complexity and performance, toHamiltonian Monte Carlo (HMC), a state-of-the-art Monte Carlo. Our resultsindicate that, for the specific application domain considered here, ourproposed solution shows good convergence performance and superior runtimecompared to HMC.

Markov chain Monte Carlo methods for hierarchical clustering of dynamic causal models