CONVERGENCE RATES OF MARKOV CHAINS IN GENETIC ANALYSIS

描述(改编自申请者摘要)：本项目的目标是 构造马氏链收敛速度的严格下界 用于遗传分析，以便马尔可夫链蒙特卡罗(MCMC) 技术可以更自信地使用。这种技术，因为它的 1989年引入分离和连锁分析，曾有过 越来越多的应用程序，人们普遍认为这是理想的 用于考虑不确定性源(例如 如等位基因频率、诊断错误、打字错误、MAP 位置不确定性、上位性、部分外显性和性别效应) 也适用于包含多个基因和多个性状的分离分析， 根据神经精神病学中预期的复杂模式进行互动 精神错乱。人们还广泛认识到，MCMC的主要弱点是 没有任何方法来确定马尔可夫链是否有足够的 汇聚在一起。虽然在文献中有许多“收敛诊断”， 它们只能提供必要条件，而不是充分条件。这个问题 当MCMC技术被普通用户应用时，变得特别令人担忧 适用于参数较多的复杂模型。寻找MCMC的严格下界 收敛速度将使使用该方法的安全指南成为可能， 并为MCMC在遗传学中更雄心勃勃的应用奠定了基础 未来。

DESCRIPTION (Adapted from applicant abstract): The objective of this project is to construct rigorous lower bounds on the convergence rates of Markov chains used in genetic analysis, in order that the Markov chain Monte Carlo (MCMC) technique can be used with greater confidence. This technique, since its introduction into segregation and linkage analysis in 1989, has had an ever increasing number of applications, and it is widely believed to be the ideal method for linkage analyses that take into account sources of uncertainty (such as allele frequencies, diagnostic misclassification, typing errors, map location uncertainities, epistasis, partial penetrance and sex effects), and also for segretation analyses that include multiple genes and multiple traits, interacting according to the complex patterns expected in neuropsychiatric disorders. It is also widely recognized that the major weakness of MCMC is the absence of any way to be certain that the Markov chain has adequately converged. While there are many "convergence diagnostics" in the literature, they can provide only necessary, not sufficient, conditions. This problem becomes 3specially worrisome when MCMC techniques are applied by general users for complex models with many parameters. Finding rigorous lower bounds on MCMC convergence rates will make possible secure guidelines for using the method, and lay the groundwork for more ambitious applications of MCMC in genetics in the future.