Modeling a Spectrum of Gaussians with SMC

[tvwenger]

Thank you for the useful insight @bob-carpenter !

@bob-carpenter

Often you can do prediction for quantities of interest without having to assign clusters. For example, you can answer questions like the probability that two data items are in the same cluster, or you can do posterior predictive data generation or prediction.

True. In my case, I’m just interested in the summary statistics across all chains, or even r-hat. If the labels are mis-matched between chains, then these statistics are meaningless.

@bob-carpenter

The only multimodality here is whether the two modes collapse and the label switching. You should be able to prevent the former by initializing them apart. The same model collapse problem can arise in SMC.

Yes, this usually works. Usually I really want a solution that always works.

The truth about my models it that, depending on the parameters, the order of the components could be irrelevant (labeling degeneracy), the order of the components could be determined uniquely (no labeling degeneracy), or a mix of the two scenarios depending on the component parameters.

Is there some other way to parameterize a model like this? Like, could the order of the components somehow be another RV to be inferred? Would that make it easier or harder to sample?