Project Euclid

Monte Carlo likelihood is becoming increasingly used where exact likelihood analysis is computationally infeasible. One area in which such likelihoods arise is that of genetic mapping, where, increasingly, researchers wish to extract additional information from limited trait data through the use of multiple genetic markers. In the genetic analysis context, Monte Carlo likelihood is most conveniently considered as a latent variable problem. Markov chain Monte Carlo provides a method of obtaining realisations of underlying latent variables simulated under a genetic model, conditional upon observed data. Hence a Monte Carlo estimate of the likelihood surface can be formed. Choice of the latent variables can be as critical as choice of sampler. In the case of very few individuals observed in each pedigree structure, such as occurs in homozygosity mapping and affected relative pair methods of genetic mapping, multilocus segregation indicators are defined and proposed as the latent variables of choice. An example of five Werner's syndrome pedigrees is given; these are a subset of the 21 pedigrees on which homozygosity mapping has recently confirmed the location of the Werner's syndrome gene on chromosome 8. However, multilocus computations on these pedigrees are impractical with standard methods of exact likelihood computation.