Mathematically Rigorous Results In Sequence Matching

BLAST计算机程序目前使用计算机模拟来给出序列匹配的统计意义的准确估计。空白序列比对的统计理论的最新进展表明，在基本的统计理论中需要进一步的严格的数学结果。该项目旨在提供这些成果。边缘效应的存在是因为实序列的长度有限，并且在序列匹配概率的渐近展开中表现为校正项。这种边缘效应在有间隙匹配的统计中可能比在无间隙匹配的统计中更重要，因为有间隙的匹配往往更长，更容易耗尽被匹配的序列。作为副产品，该项目产生了一些新的分析结果，可能有助于检测基因组标记的非随机定位。这些分析结果来自于随机和的离散时间结果的连续时间类似。

The BLAST computer program presently uses computer simulations to give accurate estimates of statistical significance for sequence matches. Recent advances in the statistical theory of gapped sequence alignments indicates a need for further rigorous mathematical results in the underlying statistical theory. This project aims to provide those results. Edge effects are present because real sequences have limited lengths and appear as a correction term in an asymptotic expansion of the probability of sequence matching. This edge effect is likely to be more important in the statistics of matching with gaps than it was in the statistics of matching without gaps, because gapped matches tend to be longer, exhausting the sequences being matched more easily. As a byproduct, this project has produced some new analytic results that are likely to be useful in detecting non-random positioning of genomic markers. These analytic results follow from continuous-time analogs for the discrete-time results for random sums.