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Nov 21, 2011 at 7:26 comment added Xi'an This is the particle MCMC method developed in the references provided in my answer. I cannot explain it in sufficient details on this forum, I am afraid. The overall principle is however to aim at a posterior based on $i$ observations at the $i$th step of the algorithm, using only the density of the $i$th observation in the update. See also Chopin (Biometrika, 2002, 89, 539-552).
Nov 19, 2011 at 14:32 comment added mahonya Thanks, I'll certainly check out the references, but I could not understand this bit in your comment: "because you can use the previous particle system as an approximation to your prior (posterior for the earlier datapoints) and only use one observation at a time" Which method are you referring to with this statement? Anyway, I'll accept your answer. As an update: I've managed to transform the problematic steps of the approach to log space, which solved my problem.
Nov 19, 2011 at 14:30 vote accept mahonya
Nov 19, 2011 at 13:28 history answered Xi'an CC BY-SA 3.0