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On the error in Laplace approximations of high-dimensional integrals (1808.06341v1)
Published 20 Aug 2018 in math.ST and stat.TH
Abstract: Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a new result on the size of the error in first- and higher-order Laplace approximations, and apply this result to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models.