ABrox—A user-friendly Python module for approximate Bayesian computation with a focus on model comparison

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

[1]  Dora Matzke,et al.  A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree Models Using Warp-III Bridge Sampling , 2018, Psychometrika.

[2]  Jeffrey N. Rouder,et al.  Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications , 2017, Psychonomic Bulletin & Review.

[3]  N. Lazar,et al.  The ASA Statement on p-Values: Context, Process, and Purpose , 2016 .

[4]  E. Wagenmakers,et al.  Model Comparison and the Principle of Parsimony , 2015 .

[5]  C. Robert,et al.  Reliable ABC model choice via random forests , 2014, Bioinform..

[6]  Jean-Marie Cornuet,et al.  DIYABC v2.0: a software to make approximate Bayesian computation inferences about population history using single nucleotide polymorphism, DNA sequence and microsatellite data , 2014, Bioinform..

[7]  Katalin Csill'ery,et al.  abc: an R package for approximate Bayesian computation (ABC) , 2011, 1106.2793.

[8]  Z. Dienes.  Bayesian Versus Orthodox Statistics: Which Side Are You On? , 2011, Perspectives on psychological science : a journal of the Association for Psychological Science.

[9]  Richard G. Everitt,et al.  Likelihood-free estimation of model evidence , 2011 .

[10]  Gaël Varoquaux,et al.  The NumPy Array: A Structure for Efficient Numerical Computation , 2011, Computing in Science & Engineering.

[11]  Erika Cule,et al.  ABC-SysBio—approximate Bayesian computation in Python with GPU support , 2010, Bioinform..

[12]  L. Excoffier,et al.  Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood , 2009, Genetics.

[13]  Anthony J Bishara,et al.  Multinomial process tree models of control and automaticity in weapon misidentification , 2009 .

[14]  Jeffrey N. Rouder,et al.  Bayesian t tests for accepting and rejecting the null hypothesis , 2009, Psychonomic bulletin & review.

[15]  David Welch,et al.  Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems , 2009, Journal of The Royal Society Interface.

[16]  C. Robert,et al.  ABC likelihood-free methods for model choice in Gibbs random fields , 2008, 0807.2767.

[17]  C. Robert,et al.  Adaptive approximate Bayesian computation , 2008, 0805.2256.

[18]  E. Wagenmakers.  A practical solution to the pervasive problems ofp values , 2007, Psychonomic bulletin & review.

[19]  Carla J. Groom,et al.  Separating multiple processes in implicit social cognition: the quad model of implicit task performance. , 2005, Journal of personality and social psychology.

[20]  L. Jacoby,et al.  Stereotypes as dominant responses: on the "social facilitation" of prejudice in anticipated public contexts. , 2003, Journal of personality and social psychology.

[21]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[22]  L. Jacoby,et al.  Prejudice and perception: the role of automatic and controlled processes in misperceiving a weapon. , 2001, Journal of personality and social psychology.

[23]  R. Nickerson,et al.  Null hypothesis significance testing: a review of an old and continuing controversy. , 2000, Psychological methods.

[24]  L. Jacoby,et al.  Stroop process dissociations: the relationship between facilitation and interference. , 1994, Journal of experimental psychology. Human perception and performance.

[25]  L. Jacoby.  A process dissociation framework: Separating automatic from intentional uses of memory , 1991 .

[26]  David M. Riefer,et al.  Multinomial Modeling and the Measurement of Cognitive Processes. , 1988 .

[27]  D. Rubin.  Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician , 1984 .

[28]  Richard D. Morey,et al.  Baysefactor: Computation of Bayes Factors for Common Designs , 2018 .

[29]  Jeffrey N. Rouder,et al.  The need for Bayesian hypothesis testing in psychological science , 2017 .

[30]  David M. Riefer,et al.  Multinomial Modeling and the Measurement of Cognitive Processes , 2001 .

[31]  L. Breiman.  Random Forests , 2001, Machine Learning.

[32]  R. Wolpert,et al.  Chapter 3: The Likelihood Principle and Generalizations , 1988 .