Source: Adv. in Appl. Probab. Volume 40, Number 2
(2008), 473-500.
The diffusion-generator approximation technique developed by De
Iorio and Griffiths (2004a) is a very useful method of
constructing importance-sampling proposal distributions. Being
based on general mathematical principles, the method can be
applied to various models in population genetics. In this paper we
extend the technique to the neutral coalescent model with
recombination, thus obtaining novel sampling distributions for the
two-locus model. We consider the case with subdivided population
structure, as well as the classic case with only a single
population. In the latter case we also consider the
importance-sampling proposal distributions suggested by Fearnhead
and Donnelly (2001), and show that their two-locus distributions
generally differ from ours. In the case of the
infinitely-many-alleles model, our approximate sampling
distributions are shown to be generally closer to the true
distributions than are Fearnhead and Donnelly's.
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