Year: 2025
Type: article
Abstract: We examine the behaviour of the Laplace and saddlepoint approximations in the high-dimensional setting, where the dimension of the model is allowed to increase with the number of observations. Approximations to the joint density, the marginal posterior density and the conditional density are considered. Our results show that under the mildest assumptions on the model, the error of the joint density approximation is O(p4∕n) if p=o(n1∕4) for the Laplace approximation and saddlepoint approximation, and O(p3∕n) if p=o(n1∕3) under additional assumptions on the second derivative of the log-likelihood. Stronger results are obtained for the approximation to the marginal posterior density.
Source: Bernoulli
DOI: 10.3150/24-bej1758
Authors: Yanbo Tang, Nancy Reid
Institutions: Imperial College London, University of Toronto
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409308270