Evaluation of marginal likelihoods via the density of states

Habeck, M

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Evaluation of marginal likelihoods via the density of states

Habeck, M. (2012). Evaluation of marginal likelihoods via the density of states. In M. Lawrence, & N. Girolami (Eds.), Artificial Intelligence and Statistics, 21-23 April 2012, La Palma, Canary Islands (pp. 486-494). Madison, WI, USA: International Machine Learning Society.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0001-8F45-1 Version Permalink: https://hdl.handle.net/21.11116/0000-0004-4C81-5

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http://proceedings.mlr.press/v22/habeck12/habeck12.pdf (Publisher version) Open Access status unknown

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Habeck, M^{1, 2, 3}, Author

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1Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, ou_1497647
2Max Planck Institute for Developmental Biology, Max Planck Society, Max-Planck-Ring 5, 72076 Tübingen, DE, ou_2421691
3Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794

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Abstract: Bayesian model comparison involves the evaluation of the marginal likelihood, the expectation of the likelihood under the prior distribution. Typically, this high-dimensional integral over all model parameters is approximated using Markov chain Monte Carlo methods. Thermodynamic integration is a popular method to estimate the marginal likelihood by using samples from annealed posteriors. Here we show that there exists a robust and flexible alternative. The new method estimates the density of states, which counts the number of states associated with a particular value of the likelihood. If the density of states is known, computation of the marginal likelihood reduces to a one- dimensional integral. We outline a maximum likelihood procedure to estimate the density of states from annealed posterior samples. We apply our method to various likelihoods and show that it is superior to thermodynamic integration in that it is more flexible with regard to the annealing schedule and the family of bridging distributions. Finally, we discuss the relation of our method with Skilling's nested sampling.

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Dates: Date issued: 2012-04

Publication Status: Issued

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Identifiers: BibTex Citekey: Habeck2012_3

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Title: Fifteenth International Conference on Artificial Intelligence and Statistics (AISTATS 2012)

Place of Event: La Palma, Canary Islands, Spain

Start-/End Date: 2012-04-21 - 2012-04-23

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Title: Artificial Intelligence and Statistics, 21-23 April 2012, La Palma, Canary Islands

Source Genre: Proceedings

Creator(s):
Lawrence, M, Editor
Girolami, N, Editor

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Publ. Info: Madison, WI, USA : International Machine Learning Society

Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 486 - 494 Identifier: -

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Title: JMLR Workshop and Conference Proceedings

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Pages: - Volume / Issue: 22 Sequence Number: - Start / End Page: - Identifier: -