Premium
Sworn testimony of the model evidence: G aussian M ixture I mportance ( GAME ) sampling
Author(s) -
Volpi Elena,
Schoups Gerrit,
Firmani Giovanni,
Vrugt Jasper A.
Publication year - 2017
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr020167
Subject(s) - sampling (signal processing) , estimator , benchmark (surveying) , computer science , gibbs sampling , mathematics , set (abstract data type) , model selection , algorithm , statistics , bayesian probability , mathematical optimization , filter (signal processing) , geodesy , computer vision , geography , programming language
What is the “best” model? The answer to this question lies in part in the eyes of the beholder, nevertheless a good model must blend rigorous theory with redeeming qualities such as parsimony and quality of fit. Model selection is used to make inferences, via weighted averaging, from a set of K candidate models,M k ; k = ( 1 , … , K ) , and help identify which model is most supported by the observed data,Y ∼ = (y ∼ 1 , … ,y ∼ n ) . Here, we introduce a new and robust estimator of the model evidence, p ( Y ∼ | M k ) , which acts as normalizing constant in the denominator of Bayes’ theorem and provides a single quantitative measure of relative support for each hypothesis that integrates model accuracy, uncertainty, and complexity. However, p ( Y ∼ | M k ) is analytically intractable for most practical modeling problems. Our method, coined GAussian Mixture importancE (GAME) sampling, uses bridge sampling of a mixture distribution fitted to samples of the posterior model parameter distribution derived from MCMC simulation. We benchmark the accuracy and reliability of GAME sampling by application to a diverse set of multivariate target distributions (up to 100 dimensions) with known values of p ( Y ∼ | M k ) and to hypothesis testing using numerical modeling of the rainfall‐runoff transformation of the Leaf River watershed in Mississippi, USA. These case studies demonstrate that GAME sampling provides robust and unbiased estimates of the evidence at a relatively small computational cost outperforming commonly used estimators. The GAME sampler is implemented in the MATLAB package of DREAM and simplifies considerably scientific inquiry through hypothesis testing and model selection.