SMC chains with multiple modes

Hi there,

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?


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No. These samples have not converged which suggest they are not reliable (if you added a fifth chain, you might get yet another peak).

This is indicative of a model with a pathological posterior, perhaps due to non-identification/ redundant parameters. Have you tried sampling with NUTS? Does it also fail miserably?

You should inspect your model to try and see where the problems are coming from.

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After investigation, I think the problem in such a case is due to the fact that there are several observables with a combined likelihood for the model, and a small number of the observables dominate by far the likelihood calculation, so there are a few high-probability peaks corresponding to multiple solutions agreeing with these particular observables. In addition, I suspect that the importance sampling criterion keeps only samples close to the - very narrow - probability peaks for each chain. Pathological is right…