ESTIMATING THE GUMBEL SCALE PARAMETER FOR LOCAL ALIGNMENT OF RANDOM SEQUENCES BY IMPORTANCE SAMPLING WITH STOPPING TIMES

• 成果类型: Article
• 署名作者: Park, Yonil; Sheetlin, Sergey; Spouge, John L.
• 署名单位: National Institutes of Health (NIH) - USA; NIH National Library of Medicine (NLM)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS663
• 发表日期: 2009
• 页码: 3697-3714
• 关键词: acid substitution matrices; approximate p-values; statistical significance

摘要

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.