2015/12/01 by Simon Barthelmé, Barthelmé, Simon, ChopinNicolas +4 · 1 citation
Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Modeling and Causal Inference #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #stat.AP #stat.CO
paper · pdf · doi:10.48550/arxiv.1512.00205
To appear in the forthcoming Handbook of Approximate Bayesian Computation (ABC), edited by S. Sisson, L. Fan, and M. Beaumont
arxiv created 2015/12/01 · openalex publication_date 2015/12/01 · arxiv updated 2015/12/02 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n factors, and combine in some way n "local" ABC approximations of each factor. This has two advantages: (a) such an approach is typically much faster than standard ABC and (b) it makes it possible to use local summary statistics (i.e. summary statistics that depend only on the data-points that correspond to a single factor), rather than global summary statistics (that depend on the complete dataset). This greatly alleviates the bias introduced by summary statistics, and even removes it entirely in situations where local summary statistics are simply the identity function. We focus on EP (Expectation-Propagation), a convenient and powerful way to combine n local approximations into a global approximation. Compared to the EP- ABC approach of Barthelmé and Chopin (2014), we present two variations, one based on the parallel EP algorithm of Cseke and Heskes (2011), which has the advantage of being implementable on a parallel architecture, and one version which bridges the gap between standard EP and parallel EP. We illustrate our approach with an expensive application of ABC, namely inference on spatial extremes.