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

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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.