Bayesian analysis for weighted mean-squared error in dual response surface optimization

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