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# Questions about calculating the genotype likelihoods

Yangyxt
Member ✭

In this website, https://software.broadinstitute.org/gatk/documentation/article.php?id=4442, you showed the formula used to calculate PL.

I can understand most of the formulas used here. But I can't understand the change on the formula when you are trying to implement G=H1H2 to P(D|G). I tried a lot of times and I cannot finish the math inference on my own. I think the formula you used to calculate P(D|G) should also be available to be generated by pure math deduction.

Therefore, if convenient, would you please show me the process of the math deduction of the formula to prove that P(D|G)=P(D|H1)/2 + P(D|H2)/2 (given a single read sequence).

Thank you!

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## Answers

Hi @Yangyxt

Take a look at this doc: https://software.broadinstitute.org/gatk/documentation/article?id=11075

Dear Grandham, Thank you for your kind response. However, I find it not answering my question. Here I paste a screenshot in this comment for better clearance of my question.

Hi @Yangyxt

This might be a question better suited for www.biostars.org or www.seqanswers.com

PS: Checkout Terra for end-to-end GATK pipelining solutions and let us know what more pipelines we can add that will make using GATK easier for you! For more details on whether this is the right fit for you checkout our blog page.Dear Grandham,

It's just we seem cannot deduce the right side of the formula from the left side given G = H1 multiplies H2.

So I'm not sure how you generate the right side of the formula. (through pure math inference or biological inference.) If it is through biological inference, would you please use more plain language to explain it to me?

Sorry for your trouble and thanks for the answer.