A Tutorial on Reversible Jump MCMC with a View toward Applications in QTL‐mapping

A tutorial derivation of the reversible jump Markov chain Monte Carlo (MCMC) algorithm is given. Various examples illustrate how reversible jump MCMC is a general framework for Metropolis‐Hastings algorithms where the proposal and the target distribution may have densities on spaces of varying dimension. It is finally discussed how reversible jump MCMC can be applied in genetics to compute the posterior distribution of the number, locations, effects, and genotypes of putative quantitative trait loci.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[3]  P. Peskun,et al.  Optimum Monte-Carlo sampling using Markov chains , 1973 .

[4]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[5]  C. Geyer,et al.  Constrained Monte Carlo Maximum Likelihood for Dependent Data , 1992 .

[6]  C. Geyer,et al.  Simulation Procedures and Likelihood Inference for Spatial Point Processes , 1994 .

[7]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[8]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[9]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[10]  J. Satagopan.  Estimating the number of quantitative trait loci via Bayesian model determination , 1996 .

[11]  M A Newton,et al.  A bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo. , 1996, Genetics.

[12]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[13]  I. Hoeschele,et al.  Mapping-linked quantitative trait loci using Bayesian analysis and Markov chain Monte Carlo algorithms. , 1997, Genetics.

[14]  S. Heath.  Markov chain Monte Carlo segregation and linkage analysis for oligogenic models. , 1997, American journal of human genetics.

[15]  Adrian F. M. Smith,et al.  Automatic Bayesian curve fitting , 1998 .

[16]  M. Sillanpää,et al.  Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data. , 1998, Genetics.

[17]  David A. Stephens,et al.  BAYESIAN ANALYSIS OF QUANTITATIVE TRAIT LOCUS DATA USING REVERSIBLE JUMP MARKOV CHAIN MONTE CARLO , 1998 .