Combining Particle MCMC with Rao-Blackwellized Monte Carlo Data Association

This recently arXived paper by Juho Kokkala and Simo Särkkä mixes a whole lot of interesting topics, from particle MCMC and Rao-Blackwellisation to particle filters, Kalman filters, and even bear population estimation. The starting setup is the state-space hidden process models where particle filters are of use. And where Andrieu, Doucet and Hollenstein (2010) introduced their particle MCMC algorithms. Rao-Blackwellisation steps have been proposed in this setup in the original paper, as well as in the ensuing discussion, like recycling rejected parameters and associated particles. The beginning of the paper is a review of the literature in this area, in particular of the Rao-Blackwellized Monte Carlo Data Association algorithm developed by Särkkä et al. (2007), of which I was not aware previously. (I alas have not followed closely enough the filtering literature in the past years.) Targets evolve independently according to Gaussian dynamics.

In the description of the model (Section 3), I feel there are prerequisites on the model I did not have (and did not check in Särkkä et al., 2007), like the meaning of targets and measurements: it seems the model assumes each measurement corresponds to a given target. More details or an example would have helped. The extension against the existing appears to be the (major) step of including unknown parameters. Due to my lack of expertise in the domain, I have no notion of the existence of similar proposals in the literature, but handling unknown parameters is definitely of direct relevance for the statistical analysis of such problems!

The simulation experiment based on an Ornstein-Uhlenbeck model is somewhat anticlimactic in that the posterior on the mean reversion rate is essentially the prior, conveniently centred at the true value, while the others remain quite wide. It may be that the experiment was too ambitious in selecting 30 simultaneous targets with only a total of 150 observations. Without highly informative priors, my beotian reaction is to doubt the feasibility of the inference. In the case of the Finnish bear study, the huge discrepancy between priors and posteriors, as well as the significant difference between the forestry expert estimations and the model predictions should be discussed, if not addressed, possibly via a simulation using the posteriors as priors. Or maybe using a hierarchical Bayes model to gather a time-wise coherence in the number of bear families. (I wonder if this technique would apply to the type of data gathered by Mohan Delampady on the West Ghats tigers…)

Overall, I am slightly intrigued by the practice of running MCMC chains in parallel and merging the outcomes with no further processing. This assumes a lot in terms of convergence and mixing on all the chains. However, convergence is never directly addressed in the paper.

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