On the Performance of Markov Chain Monte Carlo Methods on Pedigree Data and a New Algorithm

The Gibbs sampler, a Markov chain Monte Carlo (MCMC) method, has been applied to probability computation in statistical genetics since the late 1980's. But how well this algorithm works has yet to be investigated. Preliminary results presented by various researchers are very encouraging, but difficulties remain. Two of these difficulties are multimodality and reducibility, induced by complexities of a pedigree and multiallelk loci, respectively. Although the Gibbs sampler provides a way of approximating probabilities of mter€~st. a this algorithm may near a local mode for a long time, not being able to explore the whole space adequately within some practical computing time. In this paper, I evalu"'H."II" a possible SOlutl,on ate why it fails to provide good estim:ates. I present a new method, helis algorithlltl, d,esi!~n€d to Markov a the is exrilored. me'thod; plreJilllinary reslllts are pr()misin,g.