# Genotype Likelihood based Hardy-Weinberg Test

### Introduction

This page details a Hardy-Weinberg Equilibrium test based on genotype likelihoods in NGS data.

### Formulation

Hardy Weinberg equilibrium is expected in a panmictic population. The following formulation is a likelihood ratio test statistic that incorporates genotype uncertainty via genotype likelihoods. is the probability of observing the reads for individual assuming that a locus observes HWE. is the probability of observing the reads for individual assuming that a locus does not observe HWE. denotes the genotype composed of alleles and . indexes the individuals from to . is the genotype likelihood. and are the genotype frequencies estimated with and without HWE assumption respectively.

The likelihood ratio test statistic is as follows with degrees of freedom where is the number of alleles.

### Derivation

Hyun.

### Implementation

This is implemented in vt.

### Maintained by

This page is maintained by Adrian