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显著性的准确估计。缺口序列比对的统计理论的最新进展表明，需要进一步严格的数学结果的基础统计理论。本项目旨在提供这些成果。特别是，我已经开发的数学证明的限制进化的组成的高得分的片段作为布朗运动，结果，可以用来提高精度的近似的统计缺口对齐。此外，由于真实的序列具有有限的长度而存在的边缘效应作为序列匹配概率的渐近展开中的校正项出现。这种边缘效应在有空位的匹配的统计中可能比在没有空位的匹配的统计中更重要，因为有空位的匹配往往更长，更容易耗尽匹配的序列。作为一个副产品，这个项目已经产生了一些新的分析结果，可能是有用的，在检测非随机定位的基因组标记。这些分析结果遵循连续时间模拟的离散时间的随机和的结果。

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. In particular, I have developed as mathematical proofs the limiting evolution of the composition of high scoring segments as a Brownian motion, a result that can be used to improve the accuracy of approximations to the statistics of gapped alignments. In addition, the edge effects present because real sequences have limited lengths 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.