There are results that the posterior of linear Gaussian processes from is asymptotically normal (see e.g. Chib/Greenberg 1995).
Truly bimodal posterior distributions pose a separate problem as the two modes are often relatively disjoint. The standard MCMC has a hard time traversing the whole posterior in finite time. It can be done, but takes a long time. The problem typically is that people use the MCMC with the Hessian at one of the modes as the proposal. While this allows for an efficient evaluation around this mode, it makes an efficient evaluation of the second mode even more unlikely.
I attached a run of 100000 draws with acceptance rate 2% due to a wide identity matrix proposal density instead of the default inverse Hessian at the mode (requires the recent Dynare unstable snapshot or 4.4 later on). Many draws are rejected, but now the MCMC is able to jump to the second mode. The second mode is clearly visible. More draws will make it even more pronounced.
Sidenote: Mode-Jumping MCMCs work better if you know there are multiple modes you are interested in.
MA.mod (469 Bytes)
MA_PriorsAndPosteriors1.pdf (12.1 KB)