In the cases I run, with high dimensionality, it happens often that the individual SMC chains seem to probe only a very limited mode/part of the parameter space (see attached). I tried to increase the acceptance rate in order to increase the number of IMH steps, and tried to increase the threshold as well, but I keep having more or less the same result (in the sense that several chains span a narrow range and barely overlap or sometimes not even). Do you think it’s because I may have too few samples and that even though samples may update through IMH they don’t stray too much far from each other?
Another question is about the way SMC chains work together. I understand that each chain samples first from the prior, but I think I also read that SMC is inherently parallel, which should mean they are not independent, correct? In a case like the plot attached, is there value in using the different distributions of the chains together, in the sense that once combined they do correspond more or less to the global expected distribution?