Laplace and Saddlepoint Approximations in High Dimensions

07/22/2021
by   Yanbo Tang, et al.
0

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(p^4/n) if p = o(n^1/4) for the Laplace approximation and saddlepoint approximation, with improvements being possible under additional assumptions. Stronger results are obtained for the approximation to the marginal posterior density.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/20/2018

On the error in Laplace approximations of high-dimensional integrals

Laplace approximations are commonly used to approximate high-dimensional...
research
01/29/2018

Comparison of wait time approximations in distribution networks using (R,Q)-order policies

We compare different approximations for the wait time in distribution ne...
research
11/22/2019

A Novel Method of Marginalisation using Low Discrepancy Sequences for Integrated Nested Laplace Approximations

Recently, it has been shown that approximations to marginal posterior di...
research
02/13/2013

Efficient Approximations for the Marginal Likelihood of Incomplete Data Given a Bayesian Network

We discuss Bayesian methods for learning Bayesian networks when data set...
research
02/27/2013

Laplace's Method Approximations for Probabilistic Inference in Belief Networks with Continuous Variables

Laplace's method, a family of asymptotic methods used to approximate int...
research
09/09/2022

A Laplace Mixture Representation of the Horseshoe and Some Implications

The horseshoe prior, defined as a half Cauchy scale mixture of normal, p...
research
04/04/2019

A deterministic and computable Bernstein-von Mises theorem

Bernstein-von Mises results (BvM) establish that the Laplace approximati...

Please sign up or login with your details

Forgot password? Click here to reset