Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 111, Issue 514, Pages 634-645Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2015.1021006
Keywords
Control variates; Model evidence; Temperature ladder
Categories
Funding
- UK EPSRC [EP/D002060/1, EP/J016934/1]
- EU [259348]
- Royal Society Wolfson Research Merit Award
- Engineering and Physical Sciences Research Council [EP/J016934/1, EP/D002060/1] Funding Source: researchfish
- EPSRC [EP/J016934/1, EP/K034154/1] Funding Source: UKRI
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Approximation of the model evidence is well known to be challenging. One promising approach is based on thermodynamic integration, but a key concern is that the thermodynamic integral can suffer from high variability in many applications. This article considers the reduction of variance that can be achieved by exploiting control variates in this setting. Our methodology applies whenever the gradient of both the log likelihood and the log-prior with respect to the parameters can be efficiently evaluated. Results obtained on regression models and popular benchmark datasets demonstrate a significant and sometimes dramatic reduction in estimator variance and provide insight into the wider applicability of control variates to evidence estimation. Supplementary materials for this article are available online.
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