  In this paper, we address technical difficulties that arise when applying
Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform
clustering in the space of latent parameters of subject-wise generative models.
Specifically, we focus on the case where the subject-wise generative model is a
dynamic causal model (DCM) for fMRI and clusters are defined in terms of
effective brain connectivity. While an attractive approach for detecting
mechanistically interpretable subgroups in heterogeneous populations, inverting
such a hierarchical model represents a particularly challenging case, since DCM
is often characterized by high posterior correlations between its parameters.
In this context, standard MCMC schemes exhibit poor performance and extremely
slow convergence. In this paper, we investigate the properties of hierarchical
clustering which lead to the observed failure of standard MCMC schemes and
propose a solution designed to improve convergence but preserve computational
complexity. Specifically, we introduce a class of proposal distributions which
aims to capture the interdependencies between the parameters of the clustering
and subject-wise generative models and helps to reduce random walk behaviour of
the MCMC scheme. Critically, these proposal distributions only introduce a
single hyperparameter that needs to be tuned to achieve good performance. For
validation, we apply our proposed solution to synthetic and real-world datasets
and also compare it, in terms of computational complexity and performance, to
Hamiltonian Monte Carlo (HMC), a state-of-the-art Monte Carlo. Our results
indicate that, for the specific application domain considered here, our
proposed solution shows good convergence performance and superior runtime
compared to HMC.
