Approximate Bayesian computation via empirical likelihood

Approximate Bayesian computation (ABC) has now become an essential tool for the analysis of complex stochastic models when the likelihood function is unavailable. The well-established statistical method of empirical likelihood however provides another route to such settings that bypasses simulations from the model and the choices of the ABC parameters (summary statistics, distance, tolerance), while being provably convergent in the number of observations. Furthermore, avoiding model simulations leads to significant time savings in complex models, such as those used in population genetics. The ABCel algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard and quantile distributions, and time series and population genetics models.

[1]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[2]  M. Beaumont.  Approximate Bayesian Computation in Evolution and Ecology , 2010 .

[3]  Christian P Robert,et al.  Incoherent phylogeographic inference , 2010, Proceedings of the National Academy of Sciences.

[4]  Paul Fearnhead,et al.  estimating recombination from gene sequences , 2001 .

[5]  Jean-Marie Cornuet,et al.  Adaptive Multiple Importance Sampling , 2009, 0907.1254.

[6]  Ross McVinish,et al.  Improving ABC for quantile distributions , 2012, Stat. Comput..

[7]  Paul Fearnhead,et al.  Consistency of estimators of the population-scaled recombination rate. , 2003, Theoretical population biology.

[8]  M. Beaumont,et al.  ABC: a useful Bayesian tool for the analysis of population data. , 2010, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

[9]  Jean-Marie Cornuet,et al.  Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation , 2008, Bioinform..

[10]  Ngai Hang Chan,et al.  EMPIRICAL LIKELIHOOD FOR GARCH MODELS , 2006, Econometric Theory.

[11]  A. Estoup,et al.  Bayesian inferences on the recent island colonization history by the bird Zosterops lateralis lateralis , 2003, Molecular ecology.

[12]  Tobias Rydén,et al.  Hidden Markov Models , 2006 .

[13]  W. Gilchrist,et al.  Statistical Modelling with Quantile Functions , 2000 .

[14]  A. Owen.  Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[15]  Jean-Michel Marin,et al.  Approximate Bayesian computational methods , 2011, Statistics and Computing.

[16]  Steve Su,et al.  Numerical maximum log likelihood estimation for generalized lambda distributions , 2007, Comput. Stat. Data Anal..

[17]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[18]  R. Hudson.  Two-locus sampling distributions and their application. , 2001, Genetics.

[19]  Juha Karvanen,et al.  Characterizing the generalized lambda distribution by L-moments , 2008, Comput. Stat. Data Anal..

[20]  P. Donnelly,et al.  Inferring coalescence times from DNA sequence data. , 1997, Genetics.

[21]  Alan R Templeton,et al.  Coherent and incoherent inference in phylogeography and human evolution , 2010, Proceedings of the National Academy of Sciences.

[22]  李幼升,et al.  Ph , 1989 .

[23]  Anthony N. Pettitt,et al.  Likelihood-free Bayesian estimation of multivariate quantile distributions , 2011, Comput. Stat. Data Anal..

[24]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[25]  G. D. Rayner,et al.  Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions , 2002, Stat. Comput..

[26]  K. Mengersen,et al.  Robustness of ranking and selection rules using generalised g-and-k distributions , 1997 .

[27]  D. Balding,et al.  Genealogical inference from microsatellite data. , 1998, Genetics.

[28]  Jean-Marie Cornuet,et al.  GENETIC ANALYSIS OF COMPLEX DEMOGRAPHIC SCENARIOS: SPATIALLY EXPANDING POPULATIONS OF THE CANE TOAD, BUFO MARINUS , 2004, Evolution; international journal of organic evolution.

[29]  Jean-Marie Cornuet,et al.  Inference on population history and model checking using DNA sequence and microsatellite data with the software DIYABC (v1.0) , 2010, BMC Bioinformatics.

[30]  L. Excoffier,et al.  Statistical evaluation of alternative models of human evolution , 2007, Proceedings of the National Academy of Sciences.

[31]  M. Feldman,et al.  Population growth of human Y chromosomes: a study of Y chromosome microsatellites. , 1999, Molecular biology and evolution.

[32]  David Allingham,et al.  Bayesian estimation of quantile distributions , 2009, Stat. Comput..

[33]  N. Lazar.  Bayesian empirical likelihood , 2003 .

[34]  Jean-Marie Cornuet,et al.  Bridgehead Effect in the Worldwide Invasion of the Biocontrol Harlequin Ladybird , 2010, PloS one.

[35]  Paul Fearnhead,et al.  Semi-automatic Approximate Bayesian Computation , 2010 .

[36]  William H. Asquith,et al.  L-moments and TL-moments of the generalized lambda distribution , 2007, Comput. Stat. Data Anal..

[37]  Motoo Kimura,et al.  A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population*. , 1973, Genetical research.

[38]  Christian P Robert,et al.  Lack of confidence in approximate Bayesian computation model choice , 2011, Proceedings of the National Academy of Sciences.

[39]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[40]  W. Stephan,et al.  Detecting a local signature of genetic hitchhiking along a recombining chromosome. , 2002, Genetics.

[41]  Susanne M. Schennach,et al.  Bayesian exponentially tilted empirical likelihood , 2005 .

[42]  Gareth W. Peters,et al.  Bayesian Inference, Monte Carlo Sampling and Operational Risk. , 2006 .

[43]  R. Plevin,et al.  Approximate Bayesian Computation in Evolution and Ecology , 2011 .

[44]  Paul Marjoram,et al.  Markov chain Monte Carlo without likelihoods , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[45]  P. Fearnhead,et al.  A coalescent-based method for detecting and estimating recombination from gene sequences. , 2002, Genetics.