A practical guide to non-parametric approximate Bayesian computation

7 A critical task in modelling is to determine how well the theoretical assumptions encoded in 8 a model account for observations. Bayesian methods are an ideal framework for doing just this. 9 Existing approximate Bayesian computation (ABC) methods however rely on often insufficient 10 “summary statistics”. Here, I present and analyze a highly efficient extension of a recently pro11 posed (Turner et al., 2014) non-parametric approximate Bayesian computation (npABC) algorithm, 12 which circumvents this insufficiency. This method combines Markov Chain Monte Carlo simulation 13 with tools from non-parametric statistics to improve upon existing ABC methods. The primary 14 contributions of this article: 1) A more efficient implementation of this method is described, that 15 substantially improves computational performance and chain mixing. 2) Theoretical results describ16 ing the influence of methodological approximation errors on posterior estimation are discussed. In 17 particular, while this method is highly accurate, even small errors have a strong influence on model 18 comparisons when using standard statistical approaches (such as deviance information criterion). 19 Thus care must be taken when using this (or any other ABC) method for model comparison. 3) An 20 augmentation of the standard MCMC procedure, termed “Resampled MCMC”, that reduces the 21 negative influence of approximation errors on performance and accuracy, is presented. 4) In order 22 to make this method accessible to a broader audience, a number of examples of varying complexity 23 are presented along with supplementary code for their implementation. 24