Estimating the Gumbel scale parameter for local alignment of random sequences by importance sampling with stopping times

Details Estimating the Gumbel scale parameter for local alignment of random sequences by importance sampling with stopping times Estimating the Gumbel scale parameter for local alignment of random sequences by importance sampling with stopping times

2009-09-03

arxiv.org/abs/0909.0645v1

Annals of Statistics 2009, Vol. 37, No. 6A, 3697-3714

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS663 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/08-AOS663

The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase the sensitivity of searching biological sequence databases over the web. Accordingly, this article gives a novel equation for the scale parameter of the relevant Gumbel distribution. We speculate that the equation is exact, although present numerical evidence is limited. The equation involves ascending ladder variates in the global alignment of random sequences. In global alignment simulations, the ladder variates yield stopping times specifying random sequence lengths. Because of the random lengths, and because our trial distribution for importance sampling occurs on a different sample space from our target distribution, our study led to a mapping theorem, which led naturally in turn to an efficient dynamic programming algorithm for the importance sampling weights. Numerical studies using several popular alignment scoring schemes then examined the efficiency and accuracy of the resulting simulations.

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