SYKmaf - Revision history

Albrecht: Undo revision 2344 by Albrecht (talk)

2014-12-15T17:50:31Z

Undo revision 2344 by Albrecht (talk)

← Older revision		Revision as of 19:50, 15 December 2014
Line 18:		Line 18:

	<math>		<math>
	P(D\|M,f) = \prod_i P(D_i\|M,f) = ~~\prod_i~~ \sum_m \sum_{A_1,A_2} P(D_i\|G=A_1A_2)p(G=A_1A_2\|m,M)p(m),		P(D\|M,f) = \prod_i P(D_i\|M,f) = \sum_m \sum_{A_1,A_2} P(D_i\|G=A_1A_2)p(G=A_1A_2\|m,M)p(m),
	</math>		</math>

Albrecht: /* ML estimator with unknown minor */

2014-12-15T17:49:25Z

ML estimator with unknown minor

← Older revision		Revision as of 19:49, 15 December 2014
Line 18:		Line 18:

	<math>		<math>
	P(D\|M,f) = \prod_i P(D_i\|M,f) = \sum_m \sum_{A_1,A_2} P(D_i\|G=A_1A_2)p(G=A_1A_2\|m,M)p(m),		P(D\|M,f) = \prod_i P(D_i\|M,f) = \prod_i \sum_m \sum_{A_1,A_2} P(D_i\|G=A_1A_2)p(G=A_1A_2\|m,M)p(m),
	</math>		</math>

Albrecht: Created page with "==ML estimator with known minor== First infer the Major and Minor allele and then use BFGS (-doMaf 1) optimazation or the EM algorithm (..."

2014-02-26T16:36:03Z

Created page with "==ML estimator with known minor== First infer the Major and Minor allele and then use BFGS (-doMaf 1) optimazation or the EM algorithm (..."

New page

==ML estimator with known minor==

First infer the [[Inferring_Major_and_Minor_alleles|Major and Minor]] allele and then use BFGS (-doMaf 1) optimazation or the EM algorithm (-doMaf 2) to estimate the allele frequencies.

<math>
L(D|f) \propto \prod_i^N p(D_i|f) = \prod_i^N \sum_{g\in\{0,1,2\}}p(D_i|G=g)p(G=g|f)
</math>

<math>
\hat{f}=argmax_{f} L(D|f)
</math>

==ML estimator with unknown minor==

First infer the [[Inferring_Major_and_Minor_alleles|Major]] allele and then use BFGS (-doMaf 4) optimazation or the EM algorithm (-doMaf 8) to estimate the allele frequencies. Here only the Major allele needs to be known and the uncertaincy of infering the minor allele is modelled.

Let <math>\{M,m\}</math> denote the major an minor allele assuming adiallelic site, then the maximum likelihood estimate of this pair is found using the likelihood function

<math>
P(D|M,f) = \prod_i P(D_i|M,f) = \sum_m \sum_{A_1,A_2} P(D_i|G=A_1A_2)p(G=A_1A_2|m,M)p(m),
</math>