to the distribution of the haplotypes h given ρ (3)If h 1 ,…,hn are n sampled haplotypes typed at S bi-allelic loci (SNPs) LS modelled the distribution of the first haplotype as independent of ρ, i.e. all 2S possible haplotypes are equally likely, so . For the conditional distribution of h k+1 given h 1 ,…,hk, LS modelled h k+1 as an imperfect mosaic of h 1 ,…,hk through the use of a Hidden Markov Model (HMM). That is, at each SNP, h k+1 is a (possibly imperfect) copy of one of h 1 ,…,hk at that position where where the transition rates between the hidden copying states are parameterized in terms of the underlying recombination rate. The transition rates are different for each of the conditional distributions in such a way so as to mimic the property that as we condition on an increasingly larger number of haplotypes we expect to see fewer novel recombinant haplotypes. A parameterisation for the mutation rate (or emission probabilities of the HMM) is used that has similar properties (see [23] for more details).
