Literature

This page includes only references until 2011. For work after 2011, see the Publications page.

Acknowledgment: I would like to thank Professor Simon Tavaré, who courteously gave me permission to use the list of extensive references he compiled on ABC methods.

1. BACKGROUND:

A. EARLY PAPERS ON APPROXIMATING INTRACTABLE LIKELIHOODS

1984
Diggle, P. J., and R. J. Gratton.
Monte Carlo methods of inference for implicit statistical models.
Journal of the Royal Statistical Society B 46: 193–227.
(A notably early paper considering the statistical inference problem when the statistical model is known only at the level of a stochastic mechanism generating the data. As such, it addresses the same problem ABC methods aim to solve. The approach is non-Bayesian.)

Rubin, D. B.
Bayesianly justifiable and relevant frequency calcula­tions for the applied statistician.
Annals of Statististics 12: 1151–1172.

B. EARLY PAPERS IN POPULATION GENETICS WHICH LEAD TO APPROXIMATE BAYESIAN APPROACHES

1997
Fu, Y. X., and W. H. Li.
Estimating the age of the common ancestor of a sample of DNA sequences.
Molecular Biology and Evolution 14: 195–199.

Tavaré, S., D. J. Balding, R. C. Griffiths and P. Donnelly.
Inferring coalescence times from DNA sequence data.
Genetics 145: 505–518.
(Presents a rejection sampler for the posterior distribution of the parameters. In comparison to what became to known as ABC after Beaumont et al. (2002), the methods in Tavaré et al. (1997) are exact, in the sense that they employ the full data likelihood rather than a partial likelihood based on summary statistics and the data space is discrete so that the error tolerance approximation of Pritchard et al. (1999) is not needed. The paper is also interesting from philosphical perspective of Bayesian inference because it shows that apart from the specification of the priors, the single requirement to perform inference
about the parameters of a model is a computer pogram which can generate data under the model.)

1998
Weiss, G., and A. von Haeseler.
Inference of population history using a likelihood approach.
Genetics 149: 1539–1546.

C. ABC REVIEWS

2003
Marjoram, P., J. Molitor, V. Plagnol and S. Tavaré.

Markov chain Monte Carlo without likelihoods.
Proceedings of the National Academy of Sciences USA 100: 15324–15328.
(Extension of ABC from rejection sampler to Markov chain Monte Carlo sampler.)

2004
Plagnol, V., and S. Tavaré.
Approximate Bayesian computation and MCMC.
In Monte Carlo and Quasi-Monte Carlo Methods 2002., pp.99-114, edited by H. Niederreiter. Springer Verlag.

2006
Marjoram, P., and S. Tavaré.
Modern computational approaches for analysing molecular genetic variation data.
Nature Reviews Genetics 7: 759–770.

2010
Csilléry, K., M. G. B. Blum, O. E. Gaggiotti and O. François.
Approximate Bayesian Computation (ABC) in practice.
Trends in Ecology and Evolution 25: 410–418.

D. OTHER APPROACHES PARALLELLING ABC FOR PROBLEMS MANIFESTING INTRACTABLE LIKELIHOODS

Variational Bayes:
A class of methods which aim to approximate intractable integration constants that depend on the parameters of interest. Variational Bayes does not address exactly the same problem as ABC since
the likelihood is assumed to known up to the aforementioned integration constant whereas ABC has been developed for cases in which the model is only known at the level of stochastic mechanism generating the data (such as implicit statistical models of Diggle and Gratton (1984)).

See http://www.gatsby.ucl.ac.uk/vbayes/index.html for papers, software, meetings etc..

Indirect Inference:

A class of methods addressing the inference problem when the likelihoos are unkown but in contrast to ABC, the approach is non-Bayesian.

1993
Gourieroux, C., A. Montfort and E. Renault.
Indirect infer­ence.
Journal of Applied Econometrics 8: 85–118.

2004
Heggland, K., and A. Frigessi.
Estimating functions in indirect inference.
Journal of the Royal Statistical Society B 66: 447–462.

Jiang, W., and B. Turnbull.
The indirect method: Inference based on intermediate statistics: A synthesis and examples.
Statistical Science 19: 238–263.

2. PAPERS ON ABC METHODS OR ABC APPLICATIONS

1999
Pritchard, J. K., M. T. Seielstad, A. Perez-Lezaun and M. W. Feldman.
Population growth of human Y chromosomes: a study of Y chromosome microsatellites.
Molecular Biology and Evolution 16: 1791–1798.
(First use of approximate matching of the observed data and the simulated data sets, i.e., error tolerance).

2000
Markovtsova, L., P. Marjoram and S. Tavaré.
The effects of rate variation on ancestral inference in the coalescent.
Genetics 156: 1427–1436.

2002
Beaumont, M. A., W. Zhang and D. J. Balding.
Approximate Bayesian computation in population genetics.
Genetics 162: 2025–2035.
(The paper which coined the ABC term).

2003
Beaumont, M. A.
Estimation of population growth or decline in genetically monitored populations.
Genetics 164: 1139–1160.

Tallmon, D. A., G. Luikart and M. A. Beaumont.
Comparative evaluation of a new effective population size estimator based on approxi­mate Bayesian computation.
Genetics 167: 977–988.

2005
Leman, S. C., Y. Chen, J. E. Stajich, M. A. F. Noor and M. K. Uyenoyama.
Likelihoods from summary statistics: Recent diver­gence between species.
Genetics 171: 1419–1436.

2006
Hickerson, M. J., E. A. Stahl and H. A. Lessios.
Test for simultaneous divergence using approximate Bayesian computation.
Evolution 60: 2435–2453.

Padhukasahasram, B., J. D. Wall, P. Marjoram and M. Nord­borg.
Estimating recombination rates from single-nucleotide poly­morphisms using summary statistics.
Genetics 174: 1517–1528.

Peters, G. W., and S. A. Sisson.
Bayesian inference, Monte Carlo sampling and operational risk.
Journal of Operational Risk 1: 27–50.

Tanaka, M. M., A. R. Francis, F. Luciani and S. A. Sisson.
Using approximate Bayesian computation to estimate tuberculosis trans­mission parameters from genotype data.
Genetics 173: 1511–1520.

Thornton, K., and P. Andolfatto.
Approximate Bayesian in­ference reveals evidence for a recent, severe bottleneck in a Netherlands population of Drosophila melanogaster.
Genetics 172: 1607–1619.

2007
Becquet, C., and M. Przeworski.
A new approach to estimate parameters of speciation models with application to apes.
Genome Research 17: 1505–1519.

Bortot, P., S. Coles and S. Sisson.
Inference for stereological extremes.
Journal of the American Statistical Association 102: 84–92.

Fagundes, N. J. R., N. Ray, M. Beaumont, S. Neuenschwander, F. M. Salzano, S. L. Bonatto and L. Excoffier. Statistical evaluation of alternative models of human evolution.
Proceedings of the National Academy of Sciences USA 104: 17614–17619.

Pascual, M., M. P. Chapuis, F. Mestres, J. Balanya` , R. B. Huey, G. W. Gilchrist, L. Serra and A. Estoup.
Introduction history of Drosophila subobscura in the New World: a microsatellite-based survey using ABC methods.
Molecular Ecology 16: 3069–3083.

Ratmann, O., O. Jørgensen, T. Hinkley, M. Stumpf, S. Richard­son and C. Wiuf.
Using likelihood-free inference to compare evo­lutionary dynamics of the protein networks of H. pylori and P. falciparum.
Public Library of Science Computational Biology 3: e230.

Sisson, S. A.
Genetics and stochastic simulation do mix!
The American Statistician 61: 112–119.

Sisson, S. A., Y. Fan and M. M. Tanaka.
Sequential Monte Carlo without likelihoods.
Proceedings of the National Academy of Sciences USA 104: 1760–1765.

Thornton, K. R.
The neutral coalescent process for recent gene duplications and copy-number variants.
Genetics 177: 987–1000.

Wilkinson, R. D.
Bayesian inference of primate divergence times.
PhD thesis University of Cambridge.

2008
Beaumont, M. A.
Joint determination of topology, divergence times and immigration in population trees.
In Simulations, Genetics and Human Prehistory, pp. 135–154, edited by S. Matsumara, P. Forster, and C. Renfrew. McDonald Institute for Archaeological Research.

Cornuet, J., F. Santos, M. Beaumont, C. Robert, J. Marin, D. Balding, T. Guillemaud and A. Estoup.
Inferring pop­ulation history with DIY ABC: a user-friendly approach to Approximate Bayesian Computation.
Bioinformatics 24: 2713–2719.

Foll, M., M. A. Beaumont and O. Gaggiotti.
An Approximate Bayesian Computation approach to overcome biases that arise when us­ing amplified fragment length polymorphism markers to study population structure.
Genetics 179: 927–939.

Foll, M., and O. Gaggiotti.
A genome-scan method to identify selected loci appropriate for both dominant and codominant markers: a Bayesian perspective.
Genetics 180: 977–993.

François, O., M. G. B. Blum, M. Jakobsson and N. A. Rosen­berg.
Demographic history of European populations of Arabidopsis thaliana.
Public Library of Science Genetics 4: e1000075.

Joyce, P., and P. Marjoram.
Approximately sufficient statis­tics and Bayesian computation.
Statistical Applications in Genetics and Molecular Biology 7: Article 26.

Wilkinson, R. D.
Approximate bayesian computation (abc) gives exact results under the assumption of model error.
Arxiv preprint arXiv:0811.3355.

Tallmon, D. A., A. Koyuk, G. Luikart and M. A. Beaumont.
ONeSAMP: a program to estimate effective population size using approx­imate Bayesian computation.
Molecular Ecology Resources 8: 299–301.

2009
Beaumont, M. A., J. Cornuet, J. Marin and C. P. Robert.
Adaptive approximate Bayesian computation.
Biometrika 96: 983–990.

Del Moral, P., A. Doucet and A. Jasra.
An adaptive sequential Monte Carlo method for approximate Bayesian computation.

http://www.cs.ubc.ca/~arnaud/delmoral_doucet_jasra_smcabc.pdf  (Preprint).

Grelaud, A., C. P. Robert, J.-M. Marin, F. Rodolphe and J.-F. Taly.
ABC likelihood-free methods for model choice in Gibbs random fields.
Bayesian Analysis 4: 317–336.

Lane, R. O., M. Briers and K. Copsey.
Approximate Bayesian computation for source term estimation.
In Mathematics in Defence 2009.

McKinley, T., A. Cook and R. Deardon.
Inference in epidemic models without likelihoods.
The International Journal of Biostatistics 5: Article 24.

Palero, F., J. Lopes, P. Abello, E. Macpherson, M. Pascual and M. A. Beaumont.
Rapid radiation in spiny lobsters (Palinu­rus spp) as revealed by classic and ABC methods using mtDNA and
mi­crosatellite data.
BMC Evolutionary Biology 9: 263.

Peters, G., Y. Fan and S. Sisson.
On sequential Monte Carlo, partial rejection control and approximate Bayesian computation.
Arxiv preprint arXiv:0808.3466v2.

Peters, G. W., S. A. Sisson and Y. Fan.
Likelihood-free Bayesian inference for alpha-stable models.
Arxiv preprint arXiv:0911.1894.

Ratmann, O., C. Andrieu, C. Wiuf and S. Richardson.
Model criticism based on likelihood-free inference, with an application to protein network evolution.
Proceedings of the National Academy of Sciences USA 106: 10576–10581.

Secrier, M., T. Toni and M. P. H. Stumpf.
The ABC of reverse engineering biological signalling systems.
Molecular BioSystems 5: 1925– 1935.

Sisson, S. A., Y. Fan and M. M. Tanaka.
Correction for Sisson et al., Sequential monte carlo without likelihoods.
Proceedings of the National Academy of Sciences USA 106: 16889.

Sousa, V. C., M. Fritz, M. A. Beaumont and L. Chikhi.
Ap­proximate Bayesian computation without summary statistics: the case of admixture.
Genetics 181: 1507–1519.

Thornton, K. R.
Automating approximate Bayesian computation by local linear regression.
BMC Genetics 10: 35.

Toni, T., D. Welch, N. Strelkowa, A. Ipsen and M. P. H. Stumpf.
Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems.
Journal of the Royal Statistical Society Interface 6: 187–202.

Wegmann, D., C. Leuenberger and L. Excoffier.
Efficient ap­proximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood.
Genetics 182: 1207–1218.

Wilkinson, R. D., and S. Tavaré.
Estimating primate divergence times by using conditioned birth-and-death processes.
Theoretical Population Biology 75: 278–285.

2010
Bazin, E., K. J. Dawson and M. A. Beaumont.
Likelihood-free inference of population structure and local adaptation in a Bayesian hierarchical model.
Genetics 185: 000–000.

Beaumont, M. A.
Approximate Bayesian computation in evolution and ecology.
Annual Reviews of Ecology, Evolution and Systematics 41: 379-406.

Blum, M., and O. François.
Non-linear regression models for Approximate Bayesian Computation.
Statistics and Computation 20: 63–73.

Blum, M. G. B.
Choosing the summary statistics and the acceptance rate in Approximate Bayesian Computation.
In COMPSTAT 2010 – Proceedings in Computational Statistics, pp.000-000, edited by G. Saporta and Y. Lechevaille.

Blum, M. G. B., and V. C. Tran.
HIV with contact tracing: a case study in approximate Bayesian computation.
Biostatistics 11: 644-660

Blum, M.G.B.
Approximate Bayesian Computation: A Nonparametric Perspective.
Journal of the American Statistical Association 105: 1178-1187.

Drovandi, C. C., and A. N. Pettitt.
Estimation of parameters for macroparasite population evolution using approximate Bayesian com­putation.
Biometrics 67: 225–233.

Fearnhead, P., and D. Prangle.
Semi-automatic Approximate Bayesian Computation.
Arxiv preprint arXiv:1004.1112v1.

Guillemaud, T., M. A. Beaumont, M. Ciosi, J.-M. Cornuet and A. Estoup.
Inferring introduction routes of invasive species using approximate Bayesian computation on microsatellite data.
Heredity 104: 88–99.

Leuenberger, C., and D. Wegmann.
Bayesian computation and model selection without likelihoods.
Genetics 184: 243–252.

Lopes, J. S., and S. Boessenkool.
The use of approximate Bayesian computation in conservation genetics and its application in a case study on yellow-eyed penguins.
Conservation Genetics 11: 421–433.

Peters, G. W., I. Nevat, S. A. Sisson, Y. Fan and J. Yuan.
Bayesian symbol detection in wireless relay networks via likelihood-free inference.
Arxiv preprint arXiv:1007.4603v1.

Ratmann, O., C. Andrieu, C. Wiuf and S. Richardson.
Reply to Robert et al.: Model criticism informs model choice and model comparison.
Proceedings of the National Academy of Sciences USA 107: E6–E7.

Sisson, S. A., and Y. Fan.
Likelihood-free Markov chain Monte Carlo.
Arxiv preprint arXiv:1001.2058.

Sisson, S. A., G. W. Peters, M. Briers and Y. Fan.
A note on target distribution ambiguity of likelihood-free samplers.
Arxiv preprint arXiv:1005.5201.

Sottoriva, A., and S. Tavaré.
Integrating approximate Bayesian computation with complex agent-based models for cancer research.
In COMPSTAT 2010 – Proceedings in Computational Statistics, pp. 57-66, edited by G. Saporta and Y. Lechevaille. Physica Verlag.

Toni, T., and M. P. H. Stumpf.
Simulation-based model selection for dynamical systems in systems and population biology.
Bioinformatics 26: 104–110.

Walker, D. M., D. Allingham, H. W. J. Lee and M. Small.
Parameter inference in small world network disease models with approxi­mate Bayesian computational methods.
Physica A: Statistical Mechanics and its Applications 389: 540–548.

Wegmann, D., and L. Excoffier.
Bayesian inference of the demo­graphic history of chimpanzees.
Molecular Biology and Evolution 27:1425-1435.

Wegmann, D., C. Leuenberger, S. Neuenschwander and L. Ex­coffier.
ABCtoolbox: a versatile toolkit for approximate Bayesian computations.
BMC Bioinformatics 11: 116.

Wilkinson, R. D., M. Steiper, C. Soligo, R. Martin, Z. Yang and S. Tavaré.
Dating primate divergences through an integrated analysis of palaeontological and molecular data.
Systematic Biology 60: 16-31.

3. ARGUMENTS PRO/CON ABC METHODS AND DISCUSSIONS

2009
Templeton, A. R.
Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate bayesian computation.
Molecular Ecology 18: 319–331.

2010
Beaumont, M. A., R. Nielsen, C. Robert, J. Hey, O. Gaggiotti, L. Knowles, A. Estoup, M. Panchal, J. Corander, M. Hicker­son, S. A. Sisson, N. Fagundes, L. Chikhi, P. Beerli, R. Vitalis, J.-M. Cornuet, J. Huelsenbeck, M. Foll, Z. Yang, F. Rousset, D. Balding and L. Excoffier.
In defence of model-based infer­ence in phylogeography.
Molecular Ecology 19: 436–446.

Templeton, A. R.
Coalescent-based, maximum likelihood infer­ence in phylogeography.
Molecular Ecology 19: 431–435.

Templeton, A. R.
Coherent and incoherent inference in phylo­geography and human evolution.
Proceedings of the National Academy of Sciences USA 107: 6376–6381.

Berger, J.O., Fienberg, S.E., Raftery, A.E. Robert, C.P.
Incoherent phylogeographic inference.
Proceedings of the National Academy of Sciences USA 107: E157