## Optimal Design via Curve Fitting of Monte Carlo Experiments (1996)

Citations: | 18 - 4 self |

### BibTeX

@MISC{Müller96optimaldesign,

author = {Peter Müller and Giovanni Parmigiani},

title = {Optimal Design via Curve Fitting of Monte Carlo Experiments},

year = {1996}

}

### OpenURL

### Abstract

This paper explores numerical methods for stochastic optimization, with special attention to Bayesian design problems. A common and challenging situation occurs when the objective function (in Bayesian applications the expected utility) is very expensive to evaluate, perhaps because it requires integration over a space of very large dimensionality. Our goal is to explore a class of optimization algorithms designed to gain efficiency in such situations, by exploiting smoothness of the expected utility surface and borrowing information from neighboring design points. The central idea is that of implementing stochastic optimization by curve fitting of Monte Carlo samples. This is done by simulating draws from the joint parameter/sample space and evaluating the observed utilities. Fitting a smooth surface through these simulated points serves as estimate for the expected utility surface. The optimal design can then be found deterministically. In this paper we introduce a general algorithm for curve-fitting-based optimization, we discuss implementation options, and we present a consistency property for one particular implementation of the algorithm. To illustrate the advantages and limitations of curve-fitting-based optimization, and compare it with some of the alternatives, we consider in detail three important practical applications. The first is an information theoretical stopping rule for a clinical trial. The objective function is based on the expected amount of information acquired about a sub-vector of parameters of interest. The second is concerned with the timing of examination for the early detection of breast cancer in mass screening programs. It involves a two-dimensional optimization and an objective function embodying a cost-benefit analysis. The third applicat...