Mean and variance of segregating sites, Watterson's estimator, and pairwise differences under Kingman's coalescent
This entry formalizes the mean and variance of three statistics for a sample of size n ≥ 2 under Kingman's coalescent, with time scaled so that each pair of lineages coalesces at rate 1 and with mutations placed on each branch as a Poisson process of rate θ/2 per unit length (infinite sites, so every mutation is a segregating site). The genealogy is Kingman's coalescent on set partitions of the labelled sample, realized as a jump chain with independent exponential holding times, and the mutation counts on its branch segments are conditionally independent Poisson variables given the…
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