Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence

Water Resources Research
Anneli SchönigerWolfgang Nowak

Abstract

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force ...Continue Reading

References

Jul 21, 2005·Ground Water·Eileen Poeter, David Anderson
Nov 9, 2006·Ecology·William A Link, Richard J Barker
Nov 3, 2009·Ground Water·Abhishek SinghGreg Ruskauff
Oct 13, 2008·SIAM Journal on Scientific Computing : a Publication of the Society for Industrial and Applied Mathematics·Rex A KerrJoel R Stiles
Feb 1, 1982·IEEE Transactions on Pattern Analysis and Machine Intelligence·R L Kashyap

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Citations

Dec 7, 2017·EJNMMI Physics·Sandeep S V GollaRonald Boellaard
Oct 17, 2020·Environmental Science & Technology·Luciana Chavez RodriguezHolger Pagel

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Software Mentioned

DREAM
MLBMA
BMA

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