Approximate Bayesian computation using markov chain Monte Carlo simulation: DREAM(ABC)

Abstract

The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh (2013) to introduce ‘‘likelihood-free’’ inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for a residual based likelihood function in favor of one or multiple different summary statistics that exhibit superior diagnostic power. Here we propose several methodological improvements over commonly used ABC sampling methods to permit inference of complex system models. Our methodology entitled DREAM(ABC) uses the DiffeRential Evolution Adaptive Metropolis algorithm as its main building block and takes advantage of a continuous fitness function to efficiently explore the behavioral model space. Three case studies demonstrate that DREAM(ABC) is at least an order of magnitude more efficient than commonly used ABC sampling methods for more complex models. DREAM(ABC) is also more amenable to distributed, multi-processor, implementation, a prerequisite to diagnostic inference of CPU-intensive system models.