Sworn testimony of the model evidence

Sworn testimony of the model evidence: Gaussian Mixture Importance (GAME) sampling

Volpi, Elena (University of Roma Tre)
Schoups, G.H.W. (TU Delft Water Resources)
Firmani, Giovanni (University of Roma Tre)
Vrugt, Jasper A. (University of California)

2017-07-01

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, (Formula presented.), and help identify which model is most supported by the observed data, (Formula presented.). Here, we introduce a new and robust estimator of the model evidence, (Formula presented.), 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, (Formula presented.) 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 (Formula presented.) 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.

Bayesian model evidence
Bayesian model selection
bridge sampling
importance sampling
MCMC simulation

http://resolver.tudelft.nl/uuid:d0f702d6-e4e2-44c0-a87b-1a20d5a2d703

https://doi.org/10.1002/2016WR020167

2018-01-01

0043-1397

Water Resources Research, 53 (7), 6133-6158

Institutional Repository

journal article

© 2017 Elena Volpi, G.H.W. Schoups, Giovanni Firmani, Jasper A. Vrugt