Bayes Factors via Savage-Dickey Supermodels [IMA]

How could I possibly resist reblogging an arXiver post about “Savage-Dickey Supermodels”?

arXiver

http://arxiv.org/abs/1609.02186

We outline a new method to compute the Bayes Factor for model selection which bypasses the Bayesian Evidence. Our method combines multiple models into a single, nested, Supermodel using one or more hyperparameters. Since the models are now nested the Bayes Factors between the models can be efficiently computed using the Savage-Dickey Density Ratio (SDDR). In this way model selection becomes a problem of parameter estimation. We consider two ways of constructing the supermodel in detail: one based on combined models, and a second based on combined likelihoods. We report on these two approaches for a Gaussian linear model for which the Bayesian evidence can be calculated analytically and a toy nonlinear problem. Unlike the combined model approach, where a standard Monte Carlo Markov Chain (MCMC) struggles, the combined-likelihood approach fares much better in providing a reliable estimate of the log-Bayes Factor. This scheme potentially opens the way to…

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6 Responses to “Bayes Factors via Savage-Dickey Supermodels [IMA]”

  1. Ah, I have already commented this paper, but the post will only appear tomorrow!

  2. I’ll have a single, nested supermodel, please!

    With a non-linear toy!

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