Approximate Laplace importance sampling for the estimation of expected Shannon information gain in high-dimensional Bayesian design for nonlinear models

Abstract One of the major challenges in Bayesian optimal design is to approximate expected utility function an accurate and computationally efficient manner. We focus on Shannon information gain, one most widely used utilities when experimental goal parameter inference. compare performance various methods for approximating gain common nonlinear models from statistics literature, with a particular emphasis Laplace importance sampling (LIS) (ALIS), new method that aims reduce computational cost LIS. Specifically, order centre distributions LIS requires computation posterior mode each large number simulated possibilities response vector. ALIS substantially reduces amount numerical optimization required, some cases eliminating all optimization, by centering data-generating values wherever possible. Both are thoroughly compared existing approximations including Double Loop Monte Carlo, nested sampling, approximation. It found both give trade-off between mean squared error estimation, can be up 70% cheaper than Usually gives approximation but less LIS, while still being efficient, giving useful addition suite methods. However, we observed case where more accurate. In addition, first time show yield superior designs problems numbers model parameters combined co-ordinate exchange algorithm optimization.