Title: Approximate Laplace importance sampling for Bayesian design of experiments in nonlinear models
Authors: David Woods - University of Southampton (United Kingdom)
Yiolanda Englezou - University of Cyprus (Cyprus)
Tim Waite - University of Manchester (United Kingdom) [presenting]
Abstract: One of the major challenges in Bayesian optimal design is to approximate the expected utility function in an accurate and computationally efficient manner. We explore the performance of nested Monte Carlo methods for approximating the expected Shannon information gain. We emphasise Laplace Importance Sampling (LIS) and a new cheaper counterpart, Approximate Laplace Importance Sampling (ALIS). Both methods are thoroughly compared with existing approximations, including Double Loop Monte Carlo, nested importance sampling, and Laplace approximation, on a range of examples common in the Statistics literature. It is found that LIS and ALIS give an efficient trade-off between mean squared error and computational cost for utility estimation. We also show that LIS and ALIS give improved designs compared to existing methods in problems with large numbers of model parameters when combined with the approximate co-ordinate exchange algorithm for design optimization.