Approximate Bayesian computation: Difference between revisions

Revision as of 17:10, 22 July 2011

Revision as of 22:14, 23 July 2011

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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|numberissue = 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 = 104 |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 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|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=1797|doi=10.1093/bioinformatics/btq278|url=http://bioinformatics.oxfordjournals.org/cgi/content/full/26/14/1797|issue=14}}</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}}</ref>

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