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Improved techniques for sampling complex pedigrees with the Gibbs sampler.

K Joseph Abraham1, Liviu R Totir, Rohan L Fernando

  • 1Iowa State University, Ames, IA 50011, USA. abraham@iastate.edu

Genetics, Selection, Evolution : GSE
|January 11, 2007
PubMed
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Markov chain Monte Carlo (MCMC) methods, particularly the Gibbs sampler, aid linkage and segregation analyses. This study presents a novel procedure for initiating Gibbs sampling chains in complex pedigrees, improving computational efficiency.

Area of Science:

  • Computational Biology
  • Statistical Genetics
  • Bioinformatics

Background:

  • Markov chain Monte Carlo (MCMC) methods are crucial for addressing computational challenges in genetic linkage and segregation analyses.
  • The Gibbs sampler is a popular MCMC variant, but its basic form suffers from mixing and reducibility issues.
  • Initializing a Gibbs sampling chain requires a genotypic or allelic configuration consistent with pedigree marker data and possessing adequate weight in the joint distribution.

Purpose of the Study:

  • To develop a procedure for finding a suitable starting configuration for Gibbs sampling chains.
  • To address the challenge of initiating MCMC in pedigrees with a high number of loci, where exact peeling is infeasible.
  • To demonstrate the application of this procedure in implementing a blocking Gibbs sampler.

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Main Methods:

  • The study outlines a specific procedure for determining an appropriate initial genotypic or allelic configuration.
  • This method is designed for pedigrees with a large number of loci, exceeding the limits of exact peeling.
  • The procedure's utility in implementing a blocking Gibbs sampler is also explained.

Main Results:

  • A practical procedure for generating valid starting configurations for Gibbs sampling chains has been developed.
  • This method effectively overcomes the limitations of exact peeling in complex pedigrees.
  • The technique facilitates the implementation of more advanced MCMC strategies like blocking Gibbs sampling.

Conclusions:

  • The presented procedure offers a robust solution for initiating Gibbs sampling in complex genetic analyses.
  • This advancement enhances the computational feasibility and efficiency of MCMC methods in linkage and segregation studies.
  • The technique supports the development and application of sophisticated MCMC samplers for genetic data analysis.