Computational methodology for the inference of genealogical structure from genetic data.

马尔可夫链蒙特卡罗方法在统计学的许多领域引起了极大的兴趣。它们提供了只知道到一个归一化常数的概率分布的实现，因此也提供了基于观测数据的潜在变量的难以处理的概率分布的实现。这些实现可以用来获得蒙特卡罗近似，否则难以处理的似然函数和后验概率分布。这些方法允许探索模型和参数的大而复杂的假设空间。从遗传数据中估计家谱结构是一个长期存在的问题，最近随着可能提供更多信息的新型数据的出现，引起了人们新的兴趣。这类数据的可用性和数量正在迅速增加。随着越来越有必要对高度濒危物种数量严重受限的种群进行详细的种群结构评估，家谱的估计变得越来越具有实际重要性。系谱结构的连贯统计分析的主要问题在于过多的可选的系谱假设，这些假设可能与一组个体有关。马尔可夫链蒙特卡罗方法在家谱推断和种群结构估计方面的发展为解决这一复杂问题提供了一种方法。目前的奖项将支持方法论和计算性的研究。马尔可夫链蒙特卡罗方法非常灵活；为一类特殊的问题开发一种有效的方法是不寻常的。将制定和评估各种方法。将开发执行这些方法的软件，并将在一些现有数据集的情况下加以应用。该奖项由四个项目支持：统计与概率论、计算数学、系统学与种群生物学、计算生物学。

Methods of Markov chain Monte Carlo are attracting great interest in many areas of Statistics. They provide realizations from probability distributions known only up to a normalizing constant, and thus from intractable probability distributions of latent variables conditional upon observed data. These realizations can be used to obtain Monte Carlo approximants too therwise intractable likelihood functions and posterior probability distributions. The methods permit exploration of large and complex hypothesis spaces of models and parameters. Estimation of genealogical structure from genetic data is a long-standing problem, recently attracting renewed interest with the advent of new types of data that are potentially much more informative. The availability and quantity of such data are increasing rapidly. The estimation of genealogies becomes of increasing practical importance with the increasing necessity to evaluate detailed population structure in the severely numerically restricted populations of highly endangered species. The major problem in a coherent statistical analysis of genealogical structure lies in the plethora of alternative genealogical hypotheses that could relate a set of individuals. The development of the use of Markov chain Monte Carlo methods towards the inference of genealogies and the estimation of population structure offers a solution of this complex problem. The current award will support research that is both methodological and computational. Markov chain Monte CarloMethods are very flexible; developing an effective method for a particular class of problems is not routine. Methods will be developed and evaluated. Software to implement the methods will be developed, and will be applied in the context of some available data sets. This award is being supported by four programs: Statistics and Probability, Computational Mathematics, Systematics and Population Biology, and Computational Biology.