Another paper on astro ph today about parallel tempering for exploring the gravitational wave signal posterior, this one by Farr et al. But, I’m going to overlook their missed trick on the possible use of RLR/biased sampling for evidence estimation during tempering, which would genuinely allow them to compare against NS and MultiNest (which are doing both inference and marginal likelihood calculation). Instead I’m going to share an observation about tempering. While most often we think of tempering in terms of a softening of the posterior via an inverse temperature parameter there is another way to soften the posterior that can also be thought of in the same sense: tempering via partial data likelihoods. The method is exemplified in the SMC case by Chopin’s 2002 paper (he calls these “partial posteriors”), and it can easily be used to assist mixing between modes across parallel MCMC chains (and again for marginal likelihood estimation).
Perhaps its most important use remains that of exploring “big data” posteriors in the SMC case, but I’ve found it rather useful for my “small data” problems too!