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2016 Improved Laplace approximation for marginal likelihoods
Erlis Ruli, Nicola Sartori, Laura Ventura
Electron. J. Statist. 10(2): 3986-4009 (2016). DOI: 10.1214/16-EJS1218

Abstract

Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the integrand function may be far from that of the Gaussian density, and thus the standard Laplace approximation can be inaccurate. We propose an improved Laplace approximation that reduces the asymptotic error of the standard Laplace formula by one order of magnitude, thus leading to third-order accuracy. We also show, by means of practical examples of various complexity, that the proposed method is extremely accurate, even in high dimensions, improving over the standard Laplace formula. Such examples also demonstrate that the accuracy of the proposed method is comparable with that of other existing methods, which are computationally more demanding. An R implementation of the improved Laplace approximation is also provided through the R package iLaplace available on CRAN.

Citation

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Erlis Ruli. Nicola Sartori. Laura Ventura. "Improved Laplace approximation for marginal likelihoods." Electron. J. Statist. 10 (2) 3986 - 4009, 2016. https://doi.org/10.1214/16-EJS1218

Information

Received: 1 January 2016; Published: 2016
First available in Project Euclid: 29 December 2016

zbMATH: 1357.62129
MathSciNet: MR3590640
Digital Object Identifier: 10.1214/16-EJS1218

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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