Abstract
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.
Highlights
Approximate Bayesian computation (ABC) is a computational method founded in Bayesian statistics
With ABrox, we introduce a graphical user interface (GUI) which is designed to be used as a tool for all-purpose ABC, making the methods much more accessible to researchers interested in applying ABC
We demonstrate the usefulness of ABC model comparison by computing approximate Bayes factors for multinomial processing tree models (MPT) [30]
Summary
Approximate Bayesian computation (ABC) is a computational method founded in Bayesian statistics. Approximate Bayesian model comparison with ABrox “In order to profit from the practical advantages that Bayesian parameter estimation and Bayes factor hypothesis tests have to offer it is vital that the procedures of interest can be executed in accessible, user-friendly software package” They provide such a software package, called JASP [10], in order to ease the process of Bayesian hypothesis-testing. The number of accepted particles is divided by N to get a marginal posterior distribution of a model (m’) stating how likely the model is given the data at hand (D0) [11] With this metric, we can calculate the Bayes factor (BF) as the ratio of marginal likelihoods (p(D0 | m1)/p(D0 | m2)). In Eq 2, p(m2)/p(m1) is referred to the model prior odds, indicating how likely one model (m2) is relative to the other (m1) before seeing the data. p(m1 | D0)/p(m2 | D0) is the ratio of marginal posterior distributions as approximated via ABC
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