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**1 - 4**of**4**### Population structure and cryptic relatedness in genetic association studies

- Statistical Science
, 2009

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### Lecture Topics

, 2006

"... A diffusion process model of the frequency of a mutation ◦ Reversibility of a 1-dimensional diffusion process ◦ Frequency spectrum and age of a mutation General binary coalescent trees ◦ Combinatorial derivation of the age of a mutation ◦ Ewens ’ sampling formula, a combinatorial derivation ◦ Coales ..."

Abstract
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A diffusion process model of the frequency of a mutation ◦ Reversibility of a 1-dimensional diffusion process ◦ Frequency spectrum and age of a mutation General binary coalescent trees ◦ Combinatorial derivation of the age of a mutation ◦ Ewens ’ sampling formula, a combinatorial derivation ◦ Coalescent lineage distributions Gene trees and Coalescent trees ◦ DNA sequences and the infinitely-many-sites model ◦ Mutation histories, gene trees and coalescent trees ◦ Ancestral inference from gene trees Importance sampling on coalescent histories ◦ Constructing importance sampling algorithms ◦ Examples of particular models and ancestral inference The Ancestral Recombination graph ◦ Graphical description ◦ Probability calculations on the graph ◦ An MCMC algorithm for the time to the most recent ancestor along sequences A diffusion process model of the frequency of a mutation ◦ Diffusion process model of the frequency of a mutation ◦ Reversibility of a 1-dimensional diffusion process ◦ Simulation of diffusion paths ◦ Frequency spectrum and age of a mutation The population frequency of a mutation The frequency {X(t),t ≥ 0} is modelled by a diffusion process with generator L = 1 2 σ2 (x) ∂2 ∂ + µ(x) ∂x2 ∂x σ 2 (x) =x(1 − x) , µ(x) =β(x)x(1 − x) Denote ∆X(t) =X(t +∆t) − X(t) E(∆X(t) | X(t) =x) = µ(x)∆t + o(∆t) Var(∆X(t) | X(t) =x) = σ 2 (x)∆t + o(∆t)