If I have two well separated modes, they are essentially exhaustive mutually exclusive. In this case, at least naively, I can approximate the mode probability masses by averaging the density over the sample.
Is it a legitimate technique to reject chains stuck in a less probable mode based on relative mass approximated as above e.g. if the mass ratio is larger than the sample size?
Further is it legitimate to thin out the chains based on mode mass ratio approximated as above?