Model averaging in linkage analysis

AbstractMethods for genetic linkage analysis are traditionally divided into “model‐dependent” and “model‐independent,” but there may be a useful place for an intermediate class, in which a broad range of possible models is considered as a parametric family. It is possible to average over model space with an empirical Bayes prior that weights models according to their goodness of fit to epidemiologic data, such as the frequency of the disease in the population and in first‐degree relatives (and correlations with other traits in the pleiotropic case). For averaging over high‐dimensional spaces, Markov chain Monte Carlo (MCMC) has great appeal, but it has a near‐fatal flaw: it is not possible, in most cases, to provide rigorous sufficient conditions to permit the user safely to conclude that the chain has converged. A way of overcoming the convergence problem, if not of solving it, rests on a simple application of the principle of detailed balance. If the starting point of the chain has the equilibrium distribution, so will every subsequent point. The first point is chosen according to the target distribution by rejection sampling, and subsequent points by an MCMC process that has the