U-shaped And Non-parametric Bayesian Model Factorial Design

This paper deals with the design problem for recovering a response surface by using a non-parametric Bayesian approach. The criterion for selecting the designs is based on the asymptoticaverage estimation variance, and three priors for the response are speci?ed. We found the op-timal design that minimizes the criterion over the lattice designs and the U-type designs with sq-level factors and N runs. The approach we used is similar to that in Ma et al. (2003). We alsoobtained alternative expressions and lower bounds for the criterion corresponding to each of thethree Bayes models for the two-level U-type design by using the column balance and row dis-tance proposed in Fang et al. (2003).In order to search optimal designs ef?ciently ,we proposefour algorithms: forward algorithm, local search algorithm, simulated annealing algorithm andbalance-pursuit heuristic algorithm. Then we make a comparison of these four algorithms.