Monday, February 22, 2016

Refining the algorithm

I'm still not sold on Metropolis, but at least I did get my questions cleared up. In the mean time, it occurred to me that my algorithm is more complicated than it needs to be. While having a good handle on the extreme value is critical, I can build that into the sampling process by stratifying not only the data, but the prior and posterior distributions as well. In short, I'll treat each stratum as a more or less independent sample space and continue to sample from it until the distribution for that strata is sufficiently tight. Bouncing between strata will still be handled a la Gibbs sampling (by picking a value from the overall distribution and then selecting a block from the corresponding stratum.

The hangup is the "more or less independent" part. These distributions are absolutely not independent. So, while I will sample from them, I need to be able to adjust posteriors based on results in other strata. I'm banking on only having to look at adjacent strata (or, at least, only near neighbors) as opposed to the joint distribution across all of them.

Still lots of work to do.

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