[
  {"id":"beaumontApproximateBayesianComputation2010","abstract":"In the past 10 years a statistical technique, approximate Bayesian computation (ABC), has been developed that can be used to infer parameters and choose between models in the complicated scenarios that are often considered in the environmental sciences. For example, based on gene sequence and microsatellite data, the method has been used to choose between competing models of human demographic history as well as to infer growth rates, times of divergence, and other parameters. The method fits naturally in the Bayesian inferential framework, and a brief overview is given of the key concepts. Three main approaches to ABC have been developed, and these are described and compared. Although the method arose in population genetics, ABC is increasingly used in other fields, including epidemiology, systems biology, ecology, and agent-based modeling, and many of these applications are briefly described.","accessed":{"date-parts":[["2026",5,13]]},"author":[{"family":"Beaumont","given":"Mark A."}],"citation-key":"beaumontApproximateBayesianComputation2010","container-title":"Annual Review of Ecology, Evolution, and Systematics","container-title-short":"Annu. Rev. Ecol. Evol. Syst.","DOI":"10.1146/annurev-ecolsys-102209-144621","ISSN":"1543-592X, 1545-2069","issue":"1","issued":{"date-parts":[["2010",12,1]]},"language":"en","note":"Read_Status: New\nRead_Status_Date: 2026-05-13T13:19:23.883Z","page":"379–406","source":"DOI.org (Crossref)","title":"Approximate Bayesian Computation in Evolution and Ecology","type":"article-journal","URL":"https://www.annualreviews.org/doi/10.1146/annurev-ecolsys-102209-144621","volume":"41"},
  {"id":"csilleryApproximateBayesianComputation","author":[{"family":"Csilléry","given":"K"},{"family":"Lemaire","given":"L"},{"family":"François","given":"O"},{"family":"Blum","given":"MGB"}],"citation-key":"csilleryApproximateBayesianComputation","language":"en","note":"Read_Status: New\nRead_Status_Date: 2026-05-05T09:10:00.661Z","source":"Zotero","title":"Approximate Bayesian Computation (ABC) in R: A Vignette","type":"article-journal"},
  {"id":"csilleryApproximateBayesianComputation2010","abstract":"Understanding the forces that influence natural variation within and among populations has been a major objective of evolutionary biologists for decades. Motivated by the growth in computational power and data complexity, modern approaches to this question make intensive use of simulation methods. Approximate Bayesian Computation (ABC) is one of these methods. Here we review the foundations of ABC, its recent algorithmic developments, and its applications in evolutionary biology and ecology. We argue that the use of ABC should incorporate all aspects of Bayesian data analysis: formulation, fitting, and improvement of a model. ABC can be a powerful tool to make inferences with complex models if these principles are carefully applied.","author":[{"family":"Csilléry","given":"Katalin"},{"family":"Blum","given":"Michael G. B."},{"family":"Gaggiotti","given":"Oscar E."},{"family":"François","given":"Olivier"}],"citation-key":"csilleryApproximateBayesianComputation2010","container-title":"Trends in Ecology & Evolution","container-title-short":"Trends Ecol Evol","DOI":"10.1016/j.tree.2010.04.001","ISSN":"0169-5347","issue":"7","issued":{"date-parts":[["2010",7]]},"language":"eng","note":"Read_Status: New\nRead_Status_Date: 2026-04-07T13:22:11.099Z","page":"410–418","PMID":"20488578","source":"PubMed","title":"Approximate Bayesian Computation (ABC) in practice","type":"article-journal","volume":"25"},
  {"id":"fortes-limaComplexGeneticAdmixture2021","abstract":"Admixture is a fundamental evolutionary process that has influenced genetic patterns in numerous species. Maximum-likelihood approaches based on allele frequencies and linkage-disequilibrium have been extensively used to infer admixture processes from genome-wide data sets, mostly in human populations. Nevertheless, complex admixture histories, beyond one or two pulses of admixture, remain methodologically challenging to reconstruct. We developed an Approximate Bayesian Computation (ABC) framework to reconstruct highly complex admixture histories from independent genetic markers. We built the software package MetHis to simulate independent SNPs or microsatellites in a two-way admixed population for scenarios with multiple admixture pulses, monotonically decreasing or increasing recurring admixture, or combinations of these scenarios. MetHis allows users to draw model-parameter values from prior distributions set by the user, and, for each simulation, MetHis can calculate numerous summary statistics describing genetic diversity patterns and moments of the distribution of individual admixture fractions. We coupled MetHis with existing machine-learning ABC algorithms and investigated the admixture history of admixed populations. Results showed that random forest ABC scenario-choice could accurately distinguish among most complex admixture scenarios, and errors were mainly found in regions of the parameter space where scenarios were highly nested, and, thus, biologically similar. We focused on African American and Barbadian populations as two study-cases. We found that neural network ABC posterior parameter estimation was accurate and reasonably conservative under complex admixture scenarios. For both admixed populations, we found that monotonically decreasing contributions over time, from Europe and Africa, explained the observed data more accurately than multiple admixture pulses. This approach will allow for reconstructing detailed admixture histories when maximum-likelihood methods are intractable.","author":[{"family":"Fortes-Lima","given":"Cesar A."},{"family":"Laurent","given":"Romain"},{"family":"Thouzeau","given":"Valentin"},{"family":"Toupance","given":"Bruno"},{"family":"Verdu","given":"Paul"}],"citation-key":"fortes-limaComplexGeneticAdmixture2021","container-title":"Molecular Ecology Resources","container-title-short":"Mol Ecol Resour","DOI":"10.1111/1755-0998.13325","ISSN":"1755-0998","issue":"4","issued":{"date-parts":[["2021",5]]},"language":"eng","note":"Read_Status: New\nRead_Status_Date: 2026-04-07T13:23:36.649Z","page":"1098–1117","PMCID":"PMC8247995","PMID":"33452723","source":"PubMed","title":"Complex genetic admixture histories reconstructed with Approximate Bayesian Computation","type":"article-journal","volume":"21"},
  {"id":"pudloReliableABCModel2016","abstract":"Motivation: Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques.Results: We propose a novel approach based on a machine learning tool named random forests (RF) to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with RF and postponing the approximation of the posterior probability of the selected model for a second stage also relying on RF. Compared with earlier implementations of ABC model choice, the ABC RF approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least 50) and (iv) it includes an approximation of the posterior probability of the selected model. The call to RF will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets.Availability and implementation: The proposed methodology is implemented in the R package abcrf available on the CRAN.Contact:  jean-michel.marin@umontpellier.frSupplementary information:  Supplementary data are available at Bioinformatics online.","accessed":{"date-parts":[["2026",4,7]]},"author":[{"family":"Pudlo","given":"Pierre"},{"family":"Marin","given":"Jean-Michel"},{"family":"Estoup","given":"Arnaud"},{"family":"Cornuet","given":"Jean-Marie"},{"family":"Gautier","given":"Mathieu"},{"family":"Robert","given":"Christian P."}],"citation-key":"pudloReliableABCModel2016","container-title":"Bioinformatics","container-title-short":"Bioinformatics","DOI":"10.1093/bioinformatics/btv684","ISSN":"1367-4803","issue":"6","issued":{"date-parts":[["2016",3,15]]},"note":"Read_Status: New\nRead_Status_Date: 2026-04-07T13:23:20.640Z","page":"859–866","source":"Silverchair","title":"Reliable ABC model choice via random forests","type":"article-journal","URL":"https://doi.org/10.1093/bioinformatics/btv684","volume":"32"},
  {"id":"raynalABCRandomForests2019","abstract":"Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated.We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest (RF) methodology of Breiman (2001) applied in a (non-parametric) regression setting. We advocate the derivation of a new RF for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution.All methods designed here have been incorporated in the R package abcrf (version 1.7.1) available on CRAN.Supplementary data are available at Bioinformatics online.","accessed":{"date-parts":[["2026",4,7]]},"author":[{"family":"Raynal","given":"Louis"},{"family":"Marin","given":"Jean-Michel"},{"family":"Pudlo","given":"Pierre"},{"family":"Ribatet","given":"Mathieu"},{"family":"Robert","given":"Christian P"},{"family":"Estoup","given":"Arnaud"}],"citation-key":"raynalABCRandomForests2019","container-title":"Bioinformatics","container-title-short":"Bioinformatics","DOI":"10.1093/bioinformatics/bty867","ISSN":"1367-4803","issue":"10","issued":{"date-parts":[["2019",5,15]]},"note":"Read_Status: New\nRead_Status_Date: 2026-04-07T13:22:59.866Z","page":"1720–1728","source":"Silverchair","title":"ABC random forests for Bayesian parameter inference","type":"article-journal","URL":"https://doi.org/10.1093/bioinformatics/bty867","volume":"35"},
  {"id":"robertWhyApproximateBayesian","abstract":"Approximate Bayesian computation (ABC), also known as likelihood-free methods, have become a favourite tool for the analysis of complex stochastic models, primarily in population genetics but also in financial analyses. We advocated in Grelaud et al. (2009) the use of ABC for Bayesian model choice in the specific case of Gibbs random fields (GRF), relying on a sufficiency property mainly enjoyed by GRFs to show that the approach was legitimate. Despite having previously suggested the use of ABC for model choice in a wider range of models in the DIY ABC software (Cornuet et al., 2008), we present theoretical evidence that the general use of ABC for model choice is fraught with danger in the sense that no amount of computation, however large, can guarantee a proper approximation of the posterior probabilities of the models under comparison.","author":[{"family":"Robert","given":"Christian P"},{"family":"Marin","given":"Jean-Michel"},{"family":"Pillai","given":"Natesh S"}],"citation-key":"robertWhyApproximateBayesian","language":"en","note":"Read_Status: New\nRead_Status_Date: 2026-04-07T13:23:25.869Z","source":"Zotero","title":"Why approximate Bayesian computational (ABC) methods cannot handle model choice problems","type":"article-journal"},
  {"id":"turnerTutorialApproximateBayesian2012","abstract":"This tutorial explains the foundation of approximate Bayesian computation (ABC), an approach to Bayesian inference that does not require the specification of a likelihood function, and hence that can be used to estimate posterior distributions of parameters for simulation-based models. We discuss briefly the philosophy of Bayesian inference and then present several algorithms for ABC. We then apply these algorithms in a number of examples. For most of these examples, the posterior distributions are known, and so we can compare the estimated posteriors derived from ABC to the true posteriors and verify that the algorithms recover the true posteriors accurately. We also consider a popular simulation-based model of recognition memory (REM) for which the true posteriors are unknown. We conclude with a number of recommendations for applying ABC methods to solve real-world problems.","accessed":{"date-parts":[["2026",5,5]]},"author":[{"family":"Turner","given":"Brandon M."},{"family":"Van Zandt","given":"Trisha"}],"citation-key":"turnerTutorialApproximateBayesian2012","container-title":"Journal of Mathematical Psychology","container-title-short":"Journal of Mathematical Psychology","DOI":"10.1016/j.jmp.2012.02.005","ISSN":"00222496","issue":"2","issued":{"date-parts":[["2012",4]]},"language":"en","license":"https://www.elsevier.com/tdm/userlicense/1.0/","note":"Read_Status: New\nRead_Status_Date: 2026-05-05T08:49:17.248Z","page":"69–85","source":"DOI.org (Crossref)","title":"A tutorial on approximate Bayesian computation","type":"article-journal","URL":"https://linkinghub.elsevier.com/retrieve/pii/S0022249612000272","volume":"56"}
]