Mathematical Sciences: "Statistical Methods for Summarizing and Combining Gene Maps"

在过去的几年里，在开发和构建人类基因图谱方面取得了迅速的进展。因为这些图谱是从不同的数据来源和方法构建的，所以基因组数据库的搜索可能导致在同一组标记上的几个不同的图谱。 因此，重要的是将它们联合收割机（整合）以形成共识图谱，以便它们随后可用于绘制新基因。 该项目的长期目标是开发用于整合人类基因图谱的合理的基于遗传学的程序。 这包括整合来自几项研究的遗传图谱，以及将遗传图谱与各种其他图谱整合，包括物理图谱和辐射混合图谱。 作为第一步，重点是制定一个可行的统计程序，总结遗传图谱，包括总结陈述的不确定性的顺序基因座和遗传距离从每个研究;并制定统计程序整合遗传图谱从不同的独立研究。 目前的建议的具体目的是进行初步研究，以确定是否马尔可夫链蒙特卡罗（MCMC）方法在解决这些问题是可行的。 我们计划首先探索各种可能性，构建一个有效的MCMC计划从感兴趣的分布进行采样。 这包括研究先验分布的敏感性，建议分布的效率，以及确保当前应用中不可约化的现有方法的可行性。 然后，我们将考虑应该从MCMC输出中保留哪些摘要，以及应该采用哪些统计程序来联合收割机合并来自单独MCMC运行的摘要。

The past few years have seen rapid advancements in developing and constructing gene maps for humans. Because these maps are constructed from different sources of data and methods, a search of the genome databases may result in several different maps on the same group of markers. Therefore, it is important to combine (integrate) them to form consensus maps so that they can then be used for mapping new genes. The long-term objective of this project is to develop sound statistically-based procedures for integrating human gene maps. This includes integrating genetic maps from several studies, and integrating genetic maps with a variety of other maps, including physical maps and radiation hybrid maps. As a first step, the focus is to develop a workable statistical procedure for summarizing genetic maps, including summary statements of uncertainty about the order of loci and genetic distances from each study; and to develop statistical procedure for integrating genetic maps from different independent studies. The specific aim of the current proposal is to carry out a preliminary study to determine whether Markov chain Monte Carlo (MCMC) methods are feasible in addressing these issues. We plan to first explore various possibilities of constructing an efficient MCMC scheme for sampling from the distribution of interest. This includes studying sensitivities of prior distributions, efficiencies of proposal distributions, and feasibility of existing methods for ensuring irreducibility in the current application. We will then consider what summaries should be retained from MCMC outputs, and what statistical procedures should be employed to combine the summaries from separate MCMC runs.