Approximate Bayesian computation: Difference between revisions

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'''Approximate Bayesian computation (ABC)''' is a family of computational techniques in [[Bayesian statistics]]. These simulation techniques operate on summary data (such as population mean, or variance) to make broad inferences with less computation than might be required if all available data were analyzed in detail. They are especially useful in situations where evaluation of the likelihood is computationally prohibitive, or whenever suitable likelihoods are not available.

ABC methods originated in population and evolutionary genetics <ref name=Pritchard1999>{{cite journal|last = Pritchard|first = J. K.|coauthors = Seielstad, M. T., Perez-Lezaun, A., and Feldman, M. T.|title = Population Growth of Human Y Chromosomes: A Study of Y Chromosome Microsatellites|journal = Mol. Biol. Evol.|volume = 16|date = 1999|pages = 1791–1798}}</ref><ref name=Beaumont>{{cite journal|last = Beaumont|first = M. A.|coauthors = Zhang, W. and [[David Balding|Balding, D. J.]]|title = Approximate Bayesian Computation in Population Genetics|journal = Genetics|volume = 162|date = Dec 2002|pages = 2025–2035|url = http://www.genetics.org/cgi/content/abstract/162/4/2025|pmid = 12524368|issue = 4|month = Dec|day = 01}}</ref> but have recently also been introduced to the analysis of complex and stochastic [[dynamical systems]] <ref name=Toni2009>{{cite journal |author = Toni, T.; Welch, D.; Strelkowa, N.; Ipsen, A.; Stumpf, M.P.H. |year = 2009 |title = Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems | journal = Journal of the Royal Society Interface |volume = 6 |issue = 31 |pages = 187&ndash;202 |doi: = 10.1098/​rsif.2008.0172 |url=http://rsif.royalsocietypublishing.org/content/6/31/187.abstract}}</ref>.

In standard Bayesian inference the [[posterior distribution]] is given by

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The generic procedure outlined above can be computationally inefficient but ABC and likelihood-free inferential procedures can be combined with the standard computational approaches used in [[Bayesian inference]] such as [[Markov chain Monte Carlo]] <ref name=Marjoram>{{cite journal|last = Marjoram|first = P.|coauthors = Molitor, J., Plagnol, V. and Tavaré, S.|title = Markov chain Monte Carlo without likelihoods|journal = P Natl Acad Sci USA|volume = 100|number = 26|date = 2003|pages = 15324–15328|doi = 10.1073/pnas.0306899100|pmid = 14663152}} </ref> <ref name=Plagnol>{{cite journal|last = Plagnol|first = V.|coauthors = Tavaré, S.|title = Approximate Bayesian computation and MCMC|journal = Monte Carlo and Quasi-Monte Carlo Methods 2002|year = 2004|url = http://www-gene.cimr.cam.ac.uk/vplagnol/papers/vpst-web.pdf}} (The link is to a preprint.)</ref> and [[Sequential Monte Carlo method]] <ref name=Toni2009> </ref>approaches. In these frameworks ABC can be used to tackle otherwise computationally intractable problems.

An increasing number of software implementations of ABC approaches exist <ref name=Cornuet>{{cite journal|last = Cornuet|first = J-M.|coauthors = Santos, F., Beaumont, M. A., Robert, C. P., Marin, J-M., [[David Balding|Balding, D. J.]], Guillemaud, T. and Estoup, A.|title = Inferring population history with DIY ABC: a user-friendly approach to Approximate Bayesian Computation|journal = Bioinformatics|year = 2008|url = http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btn514|pmid = 18842597|doi = 10.1093/bioinformatics/btn514|volume = 24|pages = 2713}} </ref>.

==See also==