Estimation for Restriction Sites Observed by Optical Mapping Using Reversible-Jump Markov Chain Monte Carlo

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Abstract
A fundamentally new molecular-biology approach in constructing restriction maps, Optical Mapping, has been developed by Schwartz et al. (1993). Using this method restriction maps are constructed by measuring the relevant fluorescence intensity and length measurements. However, it is difficult to directly estimate the restriction site locations of single DNA molecules based on these optical mapping data because of the precision of length measurements and the unknown number of true restriction sites in the data. We propose the use of a hierarchical Bayes model based on a mixture model with normals and random noise. In this model we explicitly consider the missing observation structure of the data, such as the orientations of molecules, the allocations of cutting sites to restriction sites, and the indicator variables of whether observed cut sites are true or false. Because of the complexity of the model, the large number of missing data, and the unknown number of restriction sites, we use Reversible-Jump Markov Chain Monte Carlo (MCMC) to estimate the number and the locations of the restriction sites. Since there exists a high multimodality due to unknown orientations of molecules, we also use a combination of our MCMC approach and the flipping algorithm suggested by Dančík and Waterman (1997). The study is highly computer-intensive and the development of an efficient algorithm is required.