Bayesian Analysis for Weighted Mean-squared Error in Dual Response Surface Optimization

Abstract

Dual response surface optimization considers the mean and the variation simultaneously. The minimization of mean-squared error (MSE) is an effective approach in dual response surface optimization. Weighted MSE (WMSE) is formed by imposing the relative weights, (lambda, 1-lambda), on the squared bias and variance components of MSE. To date, a few methods have been proposed for determining lambda. The resulting lambda from these methods is either a single value or an interval. This paper aims at developing a systematic method to choose a lambda value when an interval of lambda is given. Specifically, this paper proposes a Bayesian approach to construct a probability distribution of lambda. Once the distribution of lambda is constructed, the expected value of lambda can be used to form WMSE. Copyright (C) 2009 John Wiley & Sons, Ltd.