# How worried should I be about low acceptance rate in cold chain (parallel tempering MCMC sampler)

I have a very noisy/multimodal likelihood function for a 6-parameter model. The popular emcee sampler fails miserably (no matter how many chains I use and for how long I run them, they always get stuck in local minima), but its parallel-tempered version ptemcee[*] does a pretty decent job.

Although the results are good (judged by reasonably mixed chains, and acceptable autocorrelation and effective sample size values), the acceptance rate for the cold chain is extremely low. Usually, it starts at around 30% (burn-in stage) and drops rapidly below 1%.

I've tried increasing the number of temperatures, increasing the number of chains, turning the adaptive temperature adjustment on/off, and running the sampler until the autocorrelation time drops below N/100 (where N is the length of the chains; this is a reasonable "convergence" criteria according to the emcee developer). Nothing seems to work.

My question is then: how worried should I be that the acceptance rate is so low? I'm particularly concerned about how (if) this affects my "convergence" criteria (autocorr time < N/100).

[*]: ptemcee can be described as an:

algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures.