Approximate Bayesian computation: Difference between revisions

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Revision as of 01:18, 19 September 2011

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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.|authorlink=Jonathan K. Pritchard|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|year = 1999|pages = 1791–1798|pmid = 10605120|issue = 12}}</ref><ref name=Beaumont>{{cite journal|last = Beaumont|first = M. A.|coauthors = Zhang, W. and [[David Balding|Balding, D. J.]]|title = Approximate Bayesian Computationcomputation in Populationpopulation Geneticsgenetics|journal = Genetics|volume = 162|pages = 2025–2035|url = http://www.genetics.org/cgi/content/abstract/162/4/2025|pmid = 12524368|issue = 4|date = December 1, 2002|pmc = 1462356 }}</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>

==Overview==

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For <math>\epsilon</math> sufficiently small the ABC procedure should deliver a good approximation to the true posterior, in particular if the summary statistic <math>S</math> is a [[sufficient statistic]] of the probability model. If sufficient statistics do not exist or are hard to come by, setting up a satisfying and efficient ABC approach can be challenging.

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|issue = 26|year = 2003|pages = 15324–15328|doi = 10.1073/pnas.0306899100|pmid = 14663152|issue = 26|pmc = 307566}}</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|format=PDF}} (The link is to a preprint.)</ref> and [[Sequential Monte Carlo method]] <ref name=Toni2009 /> approaches. In these frameworks ABC can be used to tackle otherwise computationally intractable problems.

While ABC and related likelihood-free methods have overwhelmingly been employed for parameter estimation, they can also be used for [[model selection]], as the whole apparatus of Bayesian model selection can be adapted to the ABC framework.<ref name= Toni2009b>{{cite journal |author = Toni, T.; Stumpf, M.P.H. |year = 2010 |title = Simulation-based model selection for dynamical systems in systems and population biology | journal = Bioinformatics |volume = 26|pages = 104104–10 |doi = 10.1093/bioinformatics/btp619 |url=http://bioinformatics.oxfordjournals.org/cgi/reprint/26/1/104.pdf|format=PDF |pmid = 19880371 |issue = 1 |pmc = 2796821 }}</ref>

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 Approximateapproximate Bayesian Computationcomputation|journal = Bioinformatics|year = 2008|url = http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btn514|pmid = 18842597|doi = 10.1093/bioinformatics/btn514|volume = 24|pages = 27132713–9|issue = 23|pmc = 2639274}}</ref><ref name=Liepe>{{cite journal|author = Liepe, J.; Barnes, C.; Cule, E.; Erguler, K.; Kirk, P.; Toni, T.; Stumpf, M.P.H.|year=2010|title=ABC-SysBio—approximate Bayesian computation in Python with GPU support|journal=Bioinformatics|volume=26|pages=17971797–9|doi=10.1093/bioinformatics/btq278|url=http://bioinformatics.oxfordjournals.org/cgi/content/full/26/14/1797|issue=14|pmid = 20591907|pmc = 2894518}}</ref><ref name=Wegmann>{{cite journal|author=Wegmann, D.; Leuenberger, C.; Neuenschwander, S.; Excoffier, L.|year=2010|title=ABCtoolbox: a versatile toolkit for approximate Bayesian computations|journal=BMC Bioinformatics|volume=11|pages=116|doi=10.1186/1471-2105-11-116|url=http://www.biomedcentral.com/1471-2105/11/116|pmid=20202215|pmc=2848233}}</ref>

Recent advances in ABC methodology, computational implementations and applications are discussed at the '''ABC in ...''' meetings: