I have changed my MCMC sampler from Ensemble to Parallel-Tempered (in emcee) in order to get an estimate of the evidence integral.
In practice this requires setting
n_temps the number of different temperatures to sample, so at the end of the run I have
n_temps chains of samples to examine where before I just had
Using multiple temperatures is presented as a way to help in exploring multimodal distributions, but my distribution is not multimodal. How many temperatures should I use if my aim is only to get an estimate of the evidence integral using thermodynamic integration?
If the answer to (1) is more than 1, then which temperature's chains should I use to infer posterior parameter distributions? Or should I just pool all of them?