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Biology statistics problem: binomial with non-constant p

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Biology statistics problem: binomial with non-constant p

Postby jonnybgood » Wed Aug 25, 2010 6:34 am

Here's the actual problem I'm faced with. Suppose a segment of dna with 100 mutations (SNPs) which occur at different frequencies from each other and between 2 different populations for the same mutation. The expected number of mutations occuring in the segment of dna is different in either population, and using this difference I can predict from which population the segment originates. I need to determine the intersection/low point between the 2 frequency curves at which I can say, to the left of this point the segment is assigned to Pop 1, to the right of this point it's assigned to Pop 2. I've managed to do this by generating thousands of simulated curves with RND. But this causes the run time to increase by half an hour, which is unacceptable. That's when I started looking into trying to calculate this curve. From what I've read, the binomial distribution is clearly what I want, except for one thing, it assumes p is constant. In my problem, every p is different. Is this possible to calculate? [I have a feeling it isn't]

PS: I've glanced over the Beta-binomial distribution, but it seems to involve a random p. In my example, I have a known value for p for each of the k trials/events, and I need to use those exact p values.
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Re: Biology statistics problem: binomial with non-constant p

Postby jonnybgood » Thu Aug 26, 2010 4:42 am

I did a poor job of explaining myself. Suppose 100 events/trials, each with a different (and known) frequency of success (p). I want to calculate the probabilities of the 100 trials resulting in 0 total succesful trials, 1 total successful trial, 2, 3, ... 99, and 100 total successful trials.
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Postby JackBean » Thu Aug 26, 2010 6:52 am

well, that's fairly simple, basic math.
For each trial you have 2 possible results, for 100 trials it's 100^2 (for x trials it's simply x^2, because for one trial 2, for two trials 2.2, for three trials 2.2.2 etc).
The positive results are for each case 100, so the probability is 100/100^2.
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Re: Biology statistics problem: binomial with non-constant p

Postby jonnybgood » Thu Aug 26, 2010 3:51 pm

Jack, each event has a different p.
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Postby JackBean » Tue Aug 31, 2010 3:36 pm

really? How is it more/less probable that you will have 0 succesful trials than that you'll have 3 of them?
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