Abstract.

A fundamentally new molecular-biology technology in constructing restriction maps, Optical Mapping, that can rapidly produce ordered restriction maps using fluorescence microscopy, 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 estimate directly 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 orientation of each molecule, the allocation of each cutting site to one of the normal distributions, and an indicator variable of whether an observed cut site is 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. The study is highly computer-intensive and the development of an efficient algorithm is required.