# Martina Favero: Some asymptotic results for the Kingman coalescent

**Time: **
Wed 2021-06-16 15.15

**Location: **
Zoom, registration required

**Lecturer: **
Martina Favero

### Abstract

We study the asymptotic behaviour of some sequences related to the Kingman coalescent, with parent dependent mutations, as the sample size grows to infinity. We start by showing that the sampling probabilities under the coalescent decay polynomially in the sample size. The degree of the polynomial depends of the number of types in the model, and its coefficient on the stationary density of the dual Wright-Fisher diffusion. Then we present a weak convergence result for a sequence of Markov chains that are composed of block counting jump chains, counting-mutations components and cost components. Finally we illustrate how these results provide a framework to analyse asymptotic properties of backward sampling algorithms, in particular the asymptotic behaviour of importance sampling weights. This talk is based on joint work with H. Hult.

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otryakhin@math.su.se
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