September 2009
Sequential Monte Carlo analysis of time series provides a direct approach to evaluating approximate model marginal likelihoods for model comparison. We exemplify this in studies of dynamic bacterial communication in systems biology, where a long sequence of state vectors follow a complicated nonlinear dynamic model with several defining biochemical parameters. MCMC methods do not mix well in these contexts, and do not lead easily to reliable estimates of model marginal likelihood. We develop an auxiliary particle filtering algorithm that simultaneously updates latent states and fixed parameters. Our algorithm takes advantage of distributed computing to carry forward a huge number of particles to ensure accuracy of the estimates. Marginal likelihood computation is developed and illustrated in evaluation of relevance of selected model components.
Keywords: Distributed Computing, Dynamic Network Models, Marginal Likelihood, Model Comparison, Particle Filtering, Systems Biology
We are grateful to Yu Tanouchi of Duke University for discussions of models in systems biology and provision of the quorum sensing model and simulations, and to Jarad Niemi for discussions of statistical and computational issues in dynamic models. Research was partially supported by grants to Duke University from the NSF (DMS-0342172) and the National Institutes of Health (grants P50-GM081883-01 and NCI U54-CA-112952-01). Aspects of the research were also partially supported by the NSF grant DMS-0635449 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the NSF or NIH.