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Atks: Redirected page to Genotype Likelihood based Hardy-Weinberg Test

2013-06-04T17:40:10Z

Redirected page to Genotype Likelihood based Hardy-Weinberg Test

← Older revision		Revision as of 13:40, 4 June 2013
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	~~=== Formulation ===~~		#REDIRECT [[Genotype Likelihood based Hardy-Weinberg Test]]

	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.~~
	~~<math>P(R_{k}\|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.~~
	~~<math>P(R_{k}\|\textbf{g})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.~~
	~~<math>G_{i,j}</math> denotes the genotype composed of alleles <math>i</math> and <math>j</math> . <math>k</math> indexes the individuals from <math>1</math> to <math> N</math> .~~
	~~<math>P(R_{k} \|G_{i,j})</math> is the genotype likelihood.~~
	~~<math>P(G_{i,j}\|\textbf{p})</math> and <math>P(G_{i,j}\|\textbf{g})</math> are the [[AF\|genotype frequencies estimated with and without HWE assumption~~]~~] respectively.~~


	~~<math>~~
	~~\begin{align}~~
	~~L(R\|g) & = \frac{\prod_{k}{P(R_{k}\|\textbf{p})}}~~
	~~{\prod_{k}{P(R_{k}\|\textbf{g})}} \\~~
	~~& = \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}\|\textbf{p})}}}~~
	~~{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}\|\textbf{g})}}} \\~~
	~~& = \frac{\prod_{k}{\sum_{i,j}{P(R_{k} \|G_{i,j} )P(G_{i,j}\|\textbf{p})}}}~~
	~~{\prod_{k}{\sum_{i,j}{P(R_{k} \|G_{i,j})P(G_{i,j}\|\textbf{g})}}} \\~~
	~~\end{align}~~
	~~</math>~~


	~~The likelihood ratio test statistic is as follows with <math>v</math> degrees of freedom where <math>n</math> is the number of alleles.~~

	~~<math>~~
	~~\begin{align}~~
	~~-2logL(R\|g) \sim X^2_v, v = \frac{n(n-1)}{2}~~
	~~\end{align}~~
	~~</math>~~

	~~=== Derivation ===~~

	~~Hyun.~~

	~~=== Maintained by ===~~

	~~This page is maintained by [mailto:atks@umich.edu Adrian~~]

Atks: /* Derivation */

2013-04-11T18:05:03Z

Derivation

← Older revision		Revision as of 14:05, 11 April 2013
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	=== Derivation ===		=== Derivation ===

	~~Adrian with much help from~~ Hyun.		Hyun.

	=== Maintained by ===		=== Maintained by ===

	This page is maintained by [mailto:atks@umich.edu Adrian]		This page is maintained by [mailto:atks@umich.edu Adrian]

Atks: /* Maintained by */

2013-04-11T17:35:10Z

Maintained by

← Older revision		Revision as of 13:35, 11 April 2013
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	=== Maintained by ===		=== Maintained by ===

	This page is maintained by [mailto:atks@umich.edu Adrian]~~, formulation by Hyun.~~		This page is maintained by [mailto:atks@umich.edu Adrian]

Atks: /* Maintained by */

2013-04-11T17:34:52Z

Maintained by

← Older revision		Revision as of 13:34, 11 April 2013
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	\end{align}		\end{align}
	</math>		</math>

			=== Derivation ===

			Adrian with much help from Hyun.

	=== Maintained by ===		=== Maintained by ===

	This page is maintained by [mailto:atks@umich.edu Adrian], formulation by Hyun.		This page is maintained by [mailto:atks@umich.edu Adrian], formulation by Hyun.

Atks at 15:04, 11 April 2013

2013-04-11T15:04:45Z

← Older revision		Revision as of 11:04, 11 April 2013
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			=== 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.		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.
	<math>P(R_{k}\|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.		<math>P(R_{k}\|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.

Atks at 15:03, 11 April 2013

2013-04-11T15:03:59Z

← Older revision		Revision as of 11:03, 11 April 2013
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	Hardy Weinberg equilibrium is expected in a panmictic population. The following formulation is a likelihood ratio test statistic that incorporates ~~the~~ genotype uncertainty via genotype likelihoods.		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.
	<math>P(R_{k}\|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.		<math>P(R_{k}\|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.
	<math>P(R_{k}\|\textbf{g})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.		<math>P(R_{k}\|\textbf{g})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.
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	<math>		<math>
	\begin{align}		\begin{align}
	L(R\|g) & = & \frac{\prod_{k}{P(R_{k}\|\textbf{p})}}		L(R\|g) & = \frac{\prod_{k}{P(R_{k}\|\textbf{p})}}
	{\prod_{k}{P(R_{k}\|\textbf{g})}} \\		{\prod_{k}{P(R_{k}\|\textbf{g})}} \\
	& = & \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}\|\textbf{p})}}}		& = \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}\|\textbf{p})}}}
	{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}\|\textbf{g})}}} \\		{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}\|\textbf{g})}}} \\
	& = & \frac{\prod_{k}{\sum_{i,j}{P(R_{k} \|G_{i,j} )P(G_{i,j}\|\textbf{p})}}}		& = \frac{\prod_{k}{\sum_{i,j}{P(R_{k} \|G_{i,j} )P(G_{i,j}\|\textbf{p})}}}
	{\prod_{k}{\sum_{i,j}{P(R_{k} \|G_{i,j})P(G_{i,j}\|\textbf{g})}}} \\		{\prod_{k}{\sum_{i,j}{P(R_{k} \|G_{i,j})P(G_{i,j}\|\textbf{g})}}} \\
	\end{align}		\end{align}

Atks: Created page with 'Hardy Weinberg equilibrium is expected in a panmictic population. The following formulation is a likelihood ratio test statistic that incorporates the genotype uncertainty via g…'

2013-04-11T14:58:47Z

Created page with 'Hardy Weinberg equilibrium is expected in a panmictic population. The following formulation is a likelihood ratio test statistic that incorporates the genotype uncertainty via g…'

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Hardy Weinberg equilibrium is expected in a panmictic population. The following formulation is a likelihood ratio test statistic that incorporates the genotype uncertainty via genotype likelihoods.
<math>P(R_{k}|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.
<math>P(R_{k}|\textbf{g})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.
<math>G_{i,j}</math> denotes the genotype composed of alleles <math>i</math> and <math>j</math> . <math>k</math> indexes the individuals from <math>1</math> to <math> N</math> .
<math>P(R_{k} |G_{i,j})</math> is the genotype likelihood.
<math>P(G_{i,j}|\textbf{p})</math> and <math>P(G_{i,j}|\textbf{g})</math> are the [[AF|genotype frequencies estimated with and without HWE assumption]] respectively.

<math>
\begin{align}
L(R|g) & = & \frac{\prod_{k}{P(R_{k}|\textbf{p})}}
{\prod_{k}{P(R_{k}|\textbf{g})}} \\
& = & \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{p})}}}
{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{g})}}} \\
& = & \frac{\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j} )P(G_{i,j}|\textbf{p})}}}
{\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j})P(G_{i,j}|\textbf{g})}}} \\
\end{align}
</math>

The likelihood ratio test statistic is as follows with <math>v</math> degrees of freedom where <math>n</math> is the number of alleles.

<math>
\begin{align}
-2logL(R|g) \sim X^2_v, v = \frac{n(n-1)}{2}
\end{align}
</math>

=== Maintained by ===

This page is maintained by [mailto:atks@umich.edu Adrian], formulation by Hyun.