Effective Sample Size & tempering/annealing

[turion]

Right now, the best approach to estimating constant parameters seems to be a stochastic diffusion process that keeps & mutates guesses for these parameters in its state, and lowers its temperature with time. This might be called "tempering" or "annealing" in the literature. There are two open research questions:

• How should the diffusion rate change? It should probably decrease with time, but also increase when the effective sample size is low. How exactly is maybe a matter of taste
• How does diffusion work for a generic parameter? One might want to make a random walk/MCMC-step on a prior (or posterior) distribution, then this seems to be RMSMC. But the implementation of mhStep in monad-bayes seems questionable. The other idea would be deriving a diffusion kernel from the parameter type.
• Probably finish RMSMC #223 first
• Finish Add effective sample size to Population tweag/monad-bayes#268 first and release

[turion]

when the effective sample size is low

To make this a more relevant criterion, one should first take the whole population PopulationT m everything and project it onto only that parameter, collapsing particles with identical values to one, and then looking at the ESS. But that would require an Eq constraint.