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Untunable Metropolis

Michael Margolis writes:

What are we to make of it when a Metropolis-Hastings step just won’t tune? That is, the acceptance rate is zero at expected-jump-size X, and way above 1/2 at X-exp(-16) (i.e., machine precision ).

I’ve solved my practical problem by writing that I would have liked to include results from a diffuse prior, but couldn’t. But I’m bothered by the poverty of my intuition. And since everything I’ve read says this is an issue of efficiency, rather than accuracy, I wonder if I could solve it just by running massive and heavily thinned chains.

My reply:

I can’t see how this could happen in a well-specified problem! I suspect it’s a bug. Otherwise try rescaling your variables so that your parameters will have values on the order of magnitude of 1.

To which Margolis responded:

I hardly wrote any of the code, so I can’t speak to the bug question — it’s binomial kriging from the R package geoRglm. And there are no covariates to scale — just the zero and one of the binomial distribution. But I will look into rescaling the spatial units forthwith.

And he tried it and it worked!

P.S. Don’t forget the folk theorem of statistical computing.