Calculating the Secrets of Life Contributions of the Mathematical Sciences to Molecular Biology (1995) / Chapter Skim
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Pages 99-104
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From page 99... ...
. LOCAL SEQUENCE COMPARISONS Alignment Given Consider many independent throws of a coin with probability p of heads, where 0 ~ p < 1 .
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This is supplied by Poisson approximation. For an appropriately chosen test length t, we see an R run of length t begins at a given position with a small probability.
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. asI amoeba Let Z denote a Poisson random variable with mean 2, so that for k =0,l,2,....
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l. We denote the total variation distance between the distributions of W and Z by W- Zll - sup I E(h(W)
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and The Poisson approximation heuristic says we should be able to approximate the distribution of W by a Poisson random variable with mean An (t)
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(4.4) Theorem 4.2 now shows us that the Poisson approximation is quite accurate for the example considered above; the probability computed is correct to within be < 10 - , that is, 0.0699 < P(Rn > 13)
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