I will present work done with Liam, Jeff Gauthier and others in EJ Chichilnisky's lab on locating retinal cones from multiple ganglion cell recordings. We write down a single hierarchical model where ganglion cell responses are modeled as independent GLMs with space-time-color separable filters and no spike history. Assuming the stimulus was gaussian ensures that the ganglion cell Spike Triggered Averages are sufficient statistics. The spatial component is then assumed to be a weighted sum of non-overlapping and appropriately placed archetypical cone receptive fields. With a benign approximation, we can integrate out the weights and focus on doing MCMC in the space of cone locations and colors only. As it turns out, this likelihood landscape has many nasty local maxima; we use parallel tempering and a few techniques specific to this problem to ensure ergodicity of the markov chain.
Doing a google scholar search on parallel tempering, also known as replica exchange, or just exchange Monte Carlo, will bring up many papers on this simple technique. Here is a review:
Parallel tempering: Theory, applications, and new perspectives