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Importance Sampling for the Infinite Sites Model

Author

Listed:
  • Hobolth Asger

    (Aarhus University)

  • Uyenoyama Marcy K

    (Duke University)

  • Wiuf Carsten

    (Aarhus University)

Abstract

Importance sampling or Markov Chain Monte Carlo sampling is required for state-of-the-art statistical analysis of population genetics data. The applicability of these sampling-based inference techniques depends crucially on the proposal distribution. In this paper, we discuss importance sampling for the infinite sites model. The infinite sites assumption is attractive because it constraints the number of possible genealogies, thereby allowing for the analysis of larger data sets. We recall the Griffiths-Tavaré and Stephens-Donnelly proposals and emphasize the relation between the latter proposal and exact sampling from the infinite alleles model. We also introduce a new proposal that takes knowledge of the ancestral state into account. The new proposal is derived from a new result on exact sampling from a single site. The methods are illustrated on simulated data sets and the data considered in Griffiths and Tavaré (1994).

Suggested Citation

  • Hobolth Asger & Uyenoyama Marcy K & Wiuf Carsten, 2008. "Importance Sampling for the Infinite Sites Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-26, October.
    • Handle: RePEc:bpj:sagmbi:v:7:y:2008:i:1:n:32
    DOI: 10.2202/1544-6115.1400
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    Citations

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    Cited by:

    1. Merle, C. & Leblois, R. & Rousset, F. & Pudlo, P., 2017. "Resampling: An improvement of importance sampling in varying population size models," Theoretical Population Biology, Elsevier, vol. 114(C), pages 70-87.
    2. Jenkins Paul A., 2012. "Stopping-Time Resampling and Population Genetic Inference under Coalescent Models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(1), pages 1-20, January.
    3. Ganapathy, Ganeshkumar & Uyenoyama, Marcy K., 2009. "Site frequency spectra from genomic SNP surveys," Theoretical Population Biology, Elsevier, vol. 75(4), pages 346-354.
    4. Hobolth, Asger & Wiuf, Carsten, 2009. "The genealogy, site frequency spectrum and ages of two nested mutant alleles," Theoretical Population Biology, Elsevier, vol. 75(4), pages 260-265.
    5. Birkner, Matthias & Blath, Jochen & Steinrücken, Matthias, 2011. "Importance sampling for Lambda-coalescents in the infinitely many sites model," Theoretical Population Biology, Elsevier, vol. 79(4), pages 155-173.
    6. Uyenoyama, Marcy K. & Takebayashi, Naoki & Kumagai, Seiji, 2020. "Allele frequency spectra in structured populations: Novel-allele probabilities under the labelled coalescent," Theoretical Population Biology, Elsevier, vol. 133(C), pages 130-140.
    7. Sainudiin, Raazesh & Véber, Amandine, 2018. "Full likelihood inference from the site frequency spectrum based on the optimal tree resolution," Theoretical Population Biology, Elsevier, vol. 124(C), pages 1-15.

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