Title: New methods for approximating the expected utility in Bayesian design for nonlinear models
Authors: Yiolanda Englezou - University of Southampton (United Kingdom) [presenting]
David Woods - University of Southampton (United Kingdom)
Tim Waite - University of Manchester (United Kingdom)
Abstract: The estimation of empirical and physical models is often performed using data collected via experimentation. Hence, the design of the experiment is crucial in determining the quality of the results. For complex models, an optimal design often depends on features, particularly model parameters, which are uncertain prior to experimentation. This dependence leads naturally to a Bayesian approach which can (a) make use of any prior information on these features, and (b) be tailored to the reduction of posterior uncertainty. Optimal Bayesian design for most realistic models is complicated by the need to approximate an analytically intractable expected utility; for example, the expected gain in Shannon information from the prior to posterior distribution. For models which are nonlinear in the uncertain parameters, this expected gain must be approximated numerically. The standard approach employs double-loop Monte Carlo integration using nested sampling from the prior distribution. Although this method is easy to implement, it produces biased approximations and is computationally expensive. We will describe, assess and compare some recent alternatives to simple Monte Carlo sampling from the prior for the approximation of expected utilities. The presented methods include combinations of features from importance sampling and Laplace approximations. Assessments will include both computational cost and the statistical qualities of the resulting approximations.