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Inference in molecular population genetics

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  • Matthew Stephens
  • Peter Donnelly

Abstract

Full likelihood‐based inference for modern population genetics data presents methodological and computational challenges. The problem is of considerable practical importance and has attracted recent attention, with the development of algorithms based on importance sampling (IS) and Markov chain Monte Carlo (MCMC) sampling. Here we introduce a new IS algorithm. The optimal proposal distribution for these problems can be characterized, and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it. We compare the new method with existing algorithms on a variety of genetic examples. Our approach substantially outperforms existing IS algorithms, with efficiency typically improved by several orders of magnitude. The new method also compares favourably with existing MCMC methods in some problems, and less favourably in others, suggesting that both IS and MCMC methods have a continuing role to play in this area. We offer insights into the relative advantages of each approach, and we discuss diagnostics in the IS framework.

Suggested Citation

  • Matthew Stephens & Peter Donnelly, 2000. "Inference in molecular population genetics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 605-635.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:4:p:605-635
    DOI: 10.1111/1467-9868.00254
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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. Larribe Fabrice & Lessard Sabin, 2008. "A Composite-Conditional-Likelihood Approach for Gene Mapping Based on Linkage Disequilibrium in Windows of Marker Loci," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-33, August.
    3. Ait Kaci Azzou, S. & Larribe, F. & Froda, S., 2016. "Inferring the demographic history from DNA sequences: An importance sampling approach based on non-homogeneous processes," Theoretical Population Biology, Elsevier, vol. 111(C), pages 16-27.
    4. 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.
    5. Spade David A., 2020. "An extended model for phylogenetic maximum likelihood based on discrete morphological characters," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 19(1), pages 1-11, February.
    6. Johndrow, James E. & Palacios, Julia A., 2019. "Exact limits of inference in coalescent models," Theoretical Population Biology, Elsevier, vol. 125(C), pages 75-93.
    7. 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.
    8. 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.
    9. Hössjer Ola & Hartman Linda & Humphreys Keith, 2009. "Ancestral Recombination Graphs under Non-Random Ascertainment, with Applications to Gene Mapping," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-44, September.
    10. Griffiths, Robert C. & Tavaré, Simon, 2018. "Ancestral inference from haplotypes and mutations," Theoretical Population Biology, Elsevier, vol. 122(C), pages 12-21.
    11. Steinrücken, Matthias & Paul, Joshua S. & Song, Yun S., 2013. "A sequentially Markov conditional sampling distribution for structured populations with migration and recombination," Theoretical Population Biology, Elsevier, vol. 87(C), pages 51-61.
    12. Vogl, Claus & Mikula, Lynette C. & Burden, Conrad J., 2020. "Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation–drift model," Theoretical Population Biology, Elsevier, vol. 134(C), pages 106-118.
    13. Blath, Jochen & Buzzoni, Eugenio & Koskela, Jere & Wilke Berenguer, Maite, 2020. "Statistical tools for seed bank detection," Theoretical Population Biology, Elsevier, vol. 132(C), pages 1-15.

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