# User:Hussein Alasadi/Notebook/stephens/2013/10/13

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(→Intro to Wen & Stephens in 2D) |
(→Intro to Wen & Stephens in 2D) |
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- | We assume that <math> y = N(\mu, \Sigma) </math>. By properties of bi-variate normal distributions <math>y_2/y_1,M</math> ~ <math>N(\mu_2 + \rho \frac{\sigma_2}{\sigma_1}(y_1 - u_1), (1-\rho^2)\sigma_1^2)</math> where <math>\rho = \frac{E[y_1y_2]}{\sigma_1 \sigma_2}</math> (for any partition of <math> y </math> into <math> y_1, y_2 </math> ). The genius of Wen & Stephens lies in the idea that the distribution of <math>y_2</math> (assign as the vector of untyped SNPs) is a function of both the panel data (<math>\mu_2</math>) and the typed SNPs <math>(y_1)</math>. | + | We assume that <math> y = N(\mu, \Sigma) </math>. By properties of bi-variate normal distributions <math>y_2/y_1,M</math> ~ <math>N(\mu_2 + \rho \frac{\sigma_2}{\sigma_1}(y_1 - u_1), (1-\rho^2)\sigma_1^2)</math> where <math>\rho = \frac{E[y_1y_2]}{\sigma_1 \sigma_2}</math> (which actually holds for any partition of <math> y </math> into <math> y_1, y_2 </math> for the multi-variate case). The genius of Wen & Stephens lies in the idea that the distribution of <math>y_2</math> (assign as the vector of untyped SNPs) is a function of both the panel data (<math>\mu_2</math>) and the typed SNPs <math>(y_1)</math>. |

== Li & Stephens in 2D == | == Li & Stephens in 2D == |

## Revision as of 15:32, 17 October 2013

analyzing pooled sequenced data with selection | Main project page Previous entry Next entry |

## Intro to Wen & Stephens in 2DSuppose we have only summary-level data for haplotypes
## Li & Stephens in 2DWe describe the Li & Stephens haplotype copying model:
Let Consider now the conditional distribution of Let We model if otherwise. ρ Now in a hidden markov model, there is also the transmission process. To mimic the effects of mutation, the copying process may be imperfect.
if |