Bayesian methods and optimal experimental design for gene mapping by radiation hybrids

Radiation hybrid mapping is a somatic cell technique for ordering human loci along a chromosome and estimating the physical distance between adjacent loci. The present paper considers a realistic model of fragment generation and retention. This model assumes that fragments are generated in the ancestral cell of a clone according to a Poisson breakage process along the chromosome. Once generated, fragments are independently retained in the clone with a common retention probability. Based on this and less restrictive models, statistical criteria such as minimum obligate breaks, maximum likelihood, and Bayesian posterior probabilities can be used to decide order. Distances can be estimated by either maximum likelihood or Bayesian posterior means. The model also permits rational design of radiation dose for optimal statistical precision. A brief examination of some real data illustrates our criteria and computational algorithms.