Mathematical Sciences: Stochastic Models in Population Genetics and DNA Sequencing

使用全变差距离的强大技术已经被开发出来，以给出特定分布与泊松分布的接近程度的界限。这些技术可以在种群遗传学中用于给出涉及选择的模型的种群参数的渐近有效估计。本研究还研究了重组DNA进化的数学模型。第三个问题是考虑新技术的统计限制，这些技术有朝一日可能被用于DNA测序。要解释目前可用的大量DNA数据，需要考虑统计可变性的数学模型。使用新的概率技术，这项研究将深入了解遗传学中三个科学相关的问题。

Powerful techniques using total variation distance have been developed to give bounds on how close a particular distribution is to the Poisson distribution. These techniques can be exploited in population genetics to give asymptotically efficient estimates of population parameters for models involving selection. This research also studies a mathematical model for the evolution of recombinant DNA. A third problem is to consider the statistical limitation of new technology which may someday be used for DNA sequencing. Interpreting the vast amount of DNA data now available requires mathematical models that take into account statistical variability. Using new probability techniques, this research will develop insight into three scientifically relevant problems in genetics.