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On the choice of prior density for the Bayesian analysis of pedigree structure

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  • Almudevar, Anthony
  • LaCombe, Jason

Abstract

This article is concerned with the choice of structural prior density for use in a fully Bayesian approach to pedigree inference. It is found that the choice of prior has considerable influence on the accuracy of the estimation. To guide this choice, a scale invariance property is introduced. Under a structural prior with this property, the marginal prior distribution of the local properties of a pedigree node (number of parents, offspring, etc.) does not depend on the number of nodes in the pedigree. Such priors are found to arise naturally by an application of the Minimum Description Length (MDL) principle, under which construction of a prior becomes equivalent to the problem of determining the length of a code required to encode a pedigree, using the principles of information theory. The approach is demonstrated using simulated and actual data, and is compared to two well-known applications, CERVUS and COLONY.

Suggested Citation

  • Almudevar, Anthony & LaCombe, Jason, 2012. "On the choice of prior density for the Bayesian analysis of pedigree structure," Theoretical Population Biology, Elsevier, vol. 81(2), pages 131-143.
    • Handle: RePEc:eee:thpobi:v:81:y:2012:i:2:p:131-143
    DOI: 10.1016/j.tpb.2011.12.003
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    References listed on IDEAS

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    1. Paul Sheridan & Takeshi Kamimura & Hidetoshi Shimodaira, 2010. "A Scale-Free Structure Prior for Graphical Models with Applications in Functional Genomics," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-12, November.
    2. Ellis, Byron & Wong, Wing Hung, 2008. "Learning Causal Bayesian Network Structures From Experimental Data," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 778-789, June.
    3. Cowell, Robert G., 2009. "Efficient maximum likelihood pedigree reconstruction," Theoretical Population Biology, Elsevier, vol. 76(4), pages 285-291.
    4. Riester, Markus & Stadler, Peter F. & Klemm, Konstantin, 2010. "Reconstruction of pedigrees in clonal plant populations," Theoretical Population Biology, Elsevier, vol. 78(2), pages 109-117.
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    Cited by:

    1. Cowell, Robert G., 2013. "A simple greedy algorithm for reconstructing pedigrees," Theoretical Population Biology, Elsevier, vol. 83(C), pages 55-63.
    2. Almudevar, Anthony, 2016. "An information theoretic approach to pedigree reconstruction," Theoretical Population Biology, Elsevier, vol. 107(C), pages 52-64.
    3. Anderson, Eric C. & Ng, Thomas C., 2016. "Bayesian pedigree inference with small numbers of single nucleotide polymorphisms via a factor-graph representation," Theoretical Population Biology, Elsevier, vol. 107(C), pages 39-51.
    4. Anderson Eric C., 2012. "Large-scale Parentage Inference with SNPs: an Efficient Algorithm for Statistical Confidence of Parent Pair Allocations," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(5), pages 1-28, November.

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