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Inference in Kingman's Coalescent with Particle Markov Chain Monte Carlo Method
Inference Kingman's Coalescent with Particle Markov Chain Monte Carlo Method
2013/6/13
We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Partic...
Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci
coalescent theory recombination asymptotic expansion sampling distribution
2011/9/19
Abstract: Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on asymptotic series has recently...
The asymptotic distribution of the length of Beta-coalescent trees
Beta-coalescent coupling, point process stable distribution Probability
2011/9/6
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
The Structure of Genealogies in the Presence of Purifying Selection: An Effective Coalescent Theory
The Structure Genealogies of Purifying Selection Effective Coalescent Theory
2010/11/15
Purifying selection distorts the structure of genealogies and hence alters the patterns of genetic variation we observe in sequence data. Although these distortions may be common, our understanding of...
A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity
coalescent Kochen-StoneLemma
2009/5/4
Let $Pi_{infty}$ be the standard $Lambda$-coalescent of Pitman, which is defined so that $Pi_{infty}(0)$ is the partition of the positive integers into singletons, and, if $Pi_n$ denotes the restricti...