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Statistical Applications in Genetics and Molecular Biology

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Volume 12, Issue 1


Volume 10 (2011)

Volume 9 (2010)

Volume 6 (2007)

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Volume 2 (2003)

Volume 1 (2002)

Approximate Bayesian computation with functional statistics

Samuel Soubeyrand / Florence Carpentier / François Guiton / Etienne K. Klein
Published Online: 2013-03-26 | DOI: https://doi.org/10.1515/sagmb-2012-0014


Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.

Keywords: dispersal model; marked point process; pairwise genetic distance; parameter estimation; spatial model; TwoGener


  • Austerlitz, F. and P. E. Smouse (2002) “Two-generation analysis of pollen flow across a landscape. iv. estimating the dispersal parameter,” Genetics, 161, 355.Google Scholar

  • Austerlitz, F., C. W. Dick, C. Dutech, E. K. Klein, S. Oddou-Muratorio, P. E. Smouse and V. L. Sork (2004) “Using genetic markers to estimate the pollen dispersal curve,” Mol. Ecol., 13, 937–954.CrossrefPubMedGoogle Scholar

  • Barnes, C. P., S. Filippi, M. P. H. Stumpf and T. Thorne (2012) “Considerate approaches to constructing summary statistics for ABC model selection,” Stat. Comput., 22, 1181–1197.CrossrefWeb of ScienceGoogle Scholar

  • Beaumont, M. A. (2010) “Approximate bayesian computation in evolution and ecology,” Annu. Rev. Ecol. Evol. Syst., 41, 379–406.CrossrefWeb of ScienceGoogle Scholar

  • Beaumont, M. A., W. Zhang and D. J. Balding (2002) “Approximate bayesian computation in population genetics,” Genetics, 162, 2025–2035.Google Scholar

  • Beaumont, M. A., J.-M. Cornuet, J.-M. Marin and C. Robert (2009) “Adaptivity for ABC algorithms: the ABC-PMC scheme,” Biometrika (in press), 96, 983–990.CrossrefGoogle Scholar

  • Blum, M. G. B. (2010a) “Approximate bayesian computation: a nonparametric perspective,” J. Am. Stat. Assoc., 205, 1178–1187.Google Scholar

  • Blum, M. G. B. (2010b) Choosing the summary statistics and the acceptance rate in approximate bayesian computation. In: Lechevallier, Y., Saporta, G. (Eds.), Proceedings of COMPSTAT’2010. Physica-Verlag, pp. 47–56.Google Scholar

  • Blum, M. G. B. and O. François (2010) “Non-linear regression models for approximate bayesian computation,” Stat. Comput., 20, 63–73.CrossrefGoogle Scholar

  • Blum, M. G. B., M. A. Nunes, D. Prangle and S. A. Sisson (2012) “A comparative review of dimension reduction methods in approximate bayesian computation,” Arxiv preprintar Xiv: 1202.3819.Google Scholar

  • Carpentier, F. (2010) Modélisations de la dispersion du pollen et estimation à partir de marqueurs génétiques, Ph.D. thesis, Université Montpellier 2.Google Scholar

  • Chilés, J.-P. and P. Delfiner (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.Google Scholar

  • Cressie, N. A. C. (1991) Statistics for Spatial Data. New York: Wiley.Google Scholar

  • Csilléry, K., M. G. B. Blum, O. E. Gaggiotti and O. François (2010) “Approximate bayesian computation (ABC) in practice,” Trends Ecol. Evol., 25, 410–418.Web of ScienceCrossrefGoogle Scholar

  • Csilléry, K., O. François and M. Blum (2011) “Abc: an R package for Approximate Bayesian Computation (ABC),” Arxiv preprint arXiv:1106.2793.Google Scholar

  • Fearnhead, P. and D. Prangle (2012) “Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation,” J. R. Stat. Soc. B, 74, 419–474.CrossrefGoogle Scholar

  • Haario, H., E. Saksman and J. Tamminen (2001) “An adaptive metropolis algorithm,” Bernoulli, 7, 223–242.CrossrefGoogle Scholar

  • Haon-Lasportes, E., F. Carpentier, O. Martin, E. K. Klein and S. Soubeyrand (2011) Conditioning on parameter point estimates in approximate bayesian computation. Research Report. INRA, Biostatistics and Spatial Processes Research Unit.Google Scholar

  • Hardy, O. J. (2003) “Estimation of pairwise relatedness between individuals and characterization of isolation-by-distance processes using dominant genetic markers,” Mol. Ecol., 12, 1577–1588.CrossrefPubMedGoogle Scholar

  • Illian, J., A. Penttinen, H. Stoyan and D. Stoyan (2008) Statistical Analysis and Modelling of Spatial PointPatterns. New York: Wiley.Google Scholar

  • Joyce, P. and P. Marjoram (2008) “Approximately sufficient statistics and bayesian computation,” Stat. Appl. Genet. Mol. Biol., 7, 1–16.Google Scholar

  • Jung, H. and P. Marjoram (2011) “Choice of summary statistic weights in approximate bayesian computation,” Stat. Appl. Genet. Mol. Biol., 10, 1–23.Web of ScienceGoogle Scholar

  • Kirkpatrick, S., C. D. Gelatt Jr. and M. P. Vecchi (1983) “Optimization by simulated annealing,” Science 220, 671–680.Google Scholar

  • Leuenberger, C. and D. Wegmann (2010) “Bayesian computation and model selection without likelihoods,” Genetics, 184, 243–252.Web of ScienceGoogle Scholar

  • Marin, J. M., P. Pudlo, C. P. Robert and R. Ryder (2011) “Approximate bayesian computational methods,” J. Stat. Comput., 22, 1167–1180.Web of ScienceGoogle Scholar

  • Marjoram, P., V. Plagnol and S. Tavaré (2003) “Markov chain Monte Carlo without likelihoods,” PNAS, 100, 15324–15328.CrossrefGoogle Scholar

  • McCulloch, C. E and S. R. Searle (2001) Generalized, Linear, and Mixed Models. New York: Wiley.Google Scholar

  • Nelder, J. A. and R. Mead (1965) “A simplex method for function minimization,” Comput. J., 7, 308–313.CrossrefGoogle Scholar

  • Nunes, M. A. and D. J. Balding (2010) “On optimal selection of summary statistics for approximate bayesian computation,” Stat. Appl. Genet. Mol. Biol., 9, 1–14.Web of ScienceGoogle Scholar

  • Oddou-Muratorio, S., E. K. Klein and F. Austerlitz (2005) “Pollen flow in the wildservice tree, sorbus torminalis (L.) Crantz. II. Pollen dispersal and heterogeneity in mating success inferred from parent–offspring analysis,” Mol. Ecol., 14, 4441–4452.CrossrefGoogle Scholar

  • Pritchard, J. K., M. T. Seielstad, A. Perez-Lezaun and M. W. Feldman (1999) “Population growth oh human y chromosomes: a study of y chromosome mibrosatellites,” Mol. Biol. Evol., 16, 1791–1798.CrossrefGoogle Scholar

  • Robledo-Arnuncio, J. J. and F. Austerlitz (2006) “Pollen dispersal in spatially aggregated populations,” The American Naturalist, 168, 500–511.Web of ScienceGoogle Scholar

  • Robledo-Arnuncio, J. J., F. Austerlitz and P. E. Smouse (2006) “A new method of estimating the pollen dispersal curve independently of effective density,” Genetics, 173, 1033–1045.Google Scholar

  • Rohatgi, V. K. (2003) Statistical Inference. Mineola, NY: Dover Publications.Google Scholar

  • Rousset, F. (1997) “Genetic differentiation and estimation of gene flow from F-statistics under isolation by distance,” Genetics, 145, 1219.Google Scholar

  • Rousset, F. (2000) “Genetic differentiation between individuals,” J. Evol. Biol., 13, 58–62.Google Scholar

  • Rousset, F. and R. Leblois (2007) “Likelihood and approximate likelihood analyses of genetic structure in a linear habitat: performance and robustness to model mis-specification,” Mol. Biol. Evol., 24, 2730–2745.Web of ScienceCrossrefGoogle Scholar

  • Rubin, D. B. (1984) “Bayesianly justifiable and relevant frequency calculations for the applied statistician,” Ann. Stat., 12, 1151–1172.CrossrefGoogle Scholar

  • Ruppert, D., M. P. Wand and R. J. Carroll (2003) Semiparametric Regression. Cambridge: Cambridge University Press.Google Scholar

  • Smouse, P. E., R. J. Dyer, R. D. Westfall and V. L. Sork (2001) “Two-generation analysis of pollen flow across a landscape .i. malegamete heterogeneity among females,” Evolution, 55, 260–271.Google Scholar

  • Stoyan, D. and H. Stoyan (1994) Fractals, Random Shapes and Pointfields: Methods of Geometrical Statistics. New York: Wiley.Google Scholar

  • Wegmann, D., C. Leuenberger and L. Excoffier (2009) “Efficient Approximate Bayesian Computation coupled with Markov chain Monte Carlo without likelihood,” Genetics, 182, 1207–1218.Web of ScienceGoogle Scholar

  • Wegmann, D., C. Leuenberger, S. Neuenschwander and L. Excoffier (2010) “Abctoolbox: a versatile toolkit for approximate bayesian computations,” BMC Bioinformatics, 11, 116.INRA, UR546 Biostatistics and Spatial Processes, F-84914 Avignon, FranceCrossrefGoogle Scholar

  • Wilson, D. J., E. Gabriel, A. J. H. Leatherbarrow, J. Cheesbrough, S. Gee, E. Bolton, A. Fox, C. A. Hart, P. J. Diggle and P. Fearnhead (2009) “Rapid evolution and the importance of recombination to the gastroenteric pathogen campylobacter jejuni,” Mol. Biol. Evol., 26, 385–397.PubMedWeb of ScienceCrossrefGoogle Scholar

About the article

Corresponding author: Samuel Soubeyrand, INRA, UR546 Biostatistics and Spatial Processes, F-84914 Avignon, France

Published Online: 2013-03-26

Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 12, Issue 1, Pages 17–37, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.1515/sagmb-2012-0014.

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