I am trying to sample from a posterior having many modes particularly far from each others using MCMC. It appears that in most cases, only one of these modes contains the 95% hpd I am looking for. I tried to implement solutions based on tempered simulating but this does not provide satisfactory results as in practice going from one "capture range" to another is to costly.
As a consequence, it appears to me that a more efficient solution would be to run many simple MCMCs from different starting points and to dive into the dominant solution by making the MCMCs interact each other. Do you know if there is some proper way to implement such an idea ?
Note: I found that paper http://lccc.eecs.berkeley.edu/Papers/dmcmc_short.pdf (Distributed Markov chain Monte Carlo, Lawrence Murray) that looks close to what I am looking for but I really do not understand the design of the function $R_i$.
[EDIT]: the lack of answers seems to indicate that there is no obvious solution to my initial problem (making several MCMCs sampling from the same target distribution from different starting point interact each other). Is that true ? why is it so complicated ? Thanks