In article <3137BE73.307F at psu.edu> henry harpending <hxh5 at psu.edu> writes:
>What is Metropolis-Hastings sampling?
>Henry Harpending, Penn State University
It's a method of importance sampling. In this case, we'd like to make a
maximum likelihood estimate of the population parameters (size, mutation
rate, growth rate) based on summing over all possible genealogies, but
there are too many of them. To overcome this problem, we selectively
sample genealogies in a way proportional to their likelihood, thus
concentrating our efforts on the relatively plausible genealogies which
will contribute most of the weight to the likelihood.
The algorithm was originally developed by Metropolis et. al. in the 50's
to do atom bomb research, but is useful in many cases where you can't
get adequate coverage with a random sample. It's closely related to the
Details (for the constant-population-size case) are in Kuhner, Yamato
and Felsenstein, Genetics 140: 1421-1430 (1995). The growing-population
case is not published yet.
Mary Kuhner mkkuhner at genetics.washington.edu