HyperModel and PTMCMCSampler

[AaronDJohnson]

Currently, NANOGrav uses an adaptive MCMC (PTMCMCSampler) to get samples from posteriors. Also, we use a form of product space sampling known as the HyperModel which is programmed to be efficient. That is, parameters are not duplicated, and only the unique parameters between models are sampled.

However, this poses an obvious problem: if we consider two very different posteriors, the sampler will adapt to one space and then upon moving to the other will be proposing samples which are adapted to the old posterior. More complicated scenarios, such as more models, will likely compound this issue.

There are two obvious solutions to this: either duplicate the parameters for each posterior (which is expensive on memory) or make a new set of adaptive parameters in PTMCMCSampler. However, what I am proposing here is to discuss which of these options, or perhaps new alternatives (RJMCMC or something else?) to approach the problem when the posteriors could be very different.