Handbook of Approximate Bayesian Computation

As the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement.The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.

IntroductionOverview of approximate Bayesian computation: S. A. Sisson, Y. Fan and M. A. BeaumontOn the history of ABC: S.TavareRegression approaches: M. G. B. BlumMonte Carlo samplers for ABC: Y. Fan and S. A. SissonSummary statistics: D. PrangleLikelihood-free model choose: J.-M. Marin, P. Pudlo, A. Estoup and C. RobertABC and indirect inference: C. C. DrovandiHigh-dimensional ABC: D. Nott, V. Ong, Y. Fan and S. A. Sisson Theoretical and methodological aspects of MCMC computations with noisy likelihoods: C. Andrieu, A.Lee and M. ViolaInformed Choices: How to calibrate ABC with hypothesis testing: O. Ratmann, A. Camacho, S. Hu and C. ColjinApproximating the likelihood in approximate Bayesian computation: C. C. Drovandi, C. Grazian, K. Mengersen and C. RobertSoftware: D.WegmannDivide and conquer in ABC: Expectation-Propagation algorithms for likelihood-free inference: S. Barthelme, N. Chopin and V. CottetSMC-ABC methods for estimation of stochastic simulation models of the limit order book: G.W. Peters, E. Panayi and F. SeptierInferences on the acquisition of multidrug resistance in Mycobacterium tuberculosis using molecular epidemiological data: G. S. Rodrigues, S. A. Sisson, M. M. TanakaABC in Systems Biology: J. Liepe and M. P. H. StumpfApplication of approximate Bayesian computation to make inference about the genetic history of Pygmy hunter-gatherers populations from Western Central Africa: A. Estoup et alABC for climate: dealing with expensive simulators: P. B. Holden, N. R. Edwards, J. Hensman and R. D. WilkinsonABC in ecological modelling: M. Fasiolo and S. N. WoodABC in Nuclear Imaging: Y. Fan, S. R. Meikle, G. Angelis and A. Sitek

Scott Sission is Professor, ARC Future Fellow and Head of Statistics in the School of Mathematics and Statistics at UNSW.Yanan Fan is a Senior Lecturer at the School of Mathematics and Statistics at UNSW.Mark Beaumont is Professor of Statistics at the University of Bristol.