conduction, convection and infrared

Having a TV this week is putting me more in touch with ordinary folks, for whose sake science maxims are subverted, e.g. "The NuWave Oven uses all 3 forms of heat transmission: conduction, convection and infrared!!". Everyone knows that "radiation" is bad for you...

As you may know, MRI used to be called NMRI, but medicine and "nuclear" don't go together.

Gibbs sampling

According to the sources I've read, Gibbs sampling doesn't really tell you how to sample... it's just divide-and-conquer: you still need to sample each variable from its full conditional.

In my problem, that would be more trouble than it's worth, since no denominators are canceling. So I'm doing good old Metropolis-Hastings, with a proposal that makes its trajectory resemble Gibbs: it randomly chooses one variable to modify, and then randomly chooses a value for that variable. In other words, the proposal is uniform over the neighbors in the "generalized hypercube"^*.

I can easily compute the posterior. In traditional MCMC, I think you would weight the samples by how often they appear. But doesn't it make more sense to directly compute the posterior in all sampled models?

Should I be using MCMC at all?
How else am I going to find the set of high-probability models? (Maybe what I want is a mode-oriented stochastic search, as my EA project did.

Believe it or not, it's my first time actually implementing MCMC.

Also, I'd like to know what proportion of the posterior mass my sampled models account for... but this is probably VeryHard to do if I can't enumerate the models (otherwise we could know whether the chain has mixed).

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^{* - what do you call a non-binary hypercube? I mean: let each node be a string in {0,...,k-1}^n, and neighborhood relation is defined by set of strings that differ in exactly 1 character. When k=2, we get the n-dim hypercube. What's the word when n>2?}.