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

过去几年，人类基因图谱的开发和构建取得了快速进展。由于这些图谱是根据不同的数据源和方法构建的，因此对基因组数据库的搜索可能会在同一组标记上产生多个不同的图谱。 因此，将它们组合（整合）以形成共识图谱非常重要，以便它们可以用于绘制新基因图谱。 该项目的长期目标是开发完善的基于统计的程序来整合人类基因图谱。 这包括整合来自多项研究的遗传图谱，以及将遗传图谱与各种其他图谱（包括物理图谱和辐射混合图谱）集成。 第一步，重点是开发一个可行的统计程序来总结遗传图谱，包括对每项研究的基因座顺序和遗传距离的不确定性的总结陈述；并开发统计程序来整合来自不同独立研究的遗传图谱。 当前提案的具体目的是进行初步研究，以确定马尔可夫链蒙特卡罗（MCMC）方法在解决这些问题时是否可行。 我们计划首先探索构建有效的 MCMC 方案以从兴趣分布中进行抽样的各种可能性。 这包括研究先验分布的敏感性、提案分布的效率以及确保当前应用中不可约性的现有方法的可行性。 然后，我们将考虑应从 MCMC 输出中保留哪些摘要，以及应采用哪些统计程序来合并来自单独 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.