At the last mostly Monte Carlo seminar, Pierre Monmarché presented a recent work on post-sampling for multimodal targets: while I consider the main problem in sampling from generic multimodal targets stands with finding the modes, rather than with exploring local aspects or estimating relative weights of said modes, this made me ponder whether or not this could be accelerated by removing chunks of the already explored modes to induce moves elsewhere, which is a form of radical, brute-force, tempering, or of Wang-Landau. As for the relative weights, a multiple move proposal can be considered, including our folding idea. Or Geyer’s inverse logistic trick. Or the similar mixture trick we used in our Biometrika paper on nested sampling. Pierre’s approach was closer to adaptive importance sampling, with a self-imposed constraint of fixed sample sizes from (approximate) distributions around each of the modes.
