Multi Response Iterative Algorithm For Optimal Design Of Linear Model And Its Implementation

Experimental design is a technique for arranging experiments economically and scientifically based on the theories of probability and statistics,which has extensive application in industry producing and the engineering design.The optimal design is the method for getting some good property of the estimation in the aspect of accuracy.In chapter 1,we introduce the general situation about the whole paper. Then in chapter 2, we discuss the optimal iteration algorithm of multiresponse in the Bayesian framework. We can obtain the posterior distribution with respect to a given prior information, and the posterior co-variance matrix yields the multiresponse bayesian information matrix. By using the directional derivative,we can get the L_B^- and D_B^- optimal equivalence theorems,the lower bounds for the efficiency and the iteration algorithm for the construction of exact optimal design. In chapter 3,we discuss the sequential generation of multiresponse A-optimal designs when the variance-covariance matrix is not known. If∑is not known, a consistent estimator of∑can be used to construct a sequence of design measures which converges in probability to A-optimal design. The final result is not interfered by the random change of the sample vector. In chapter 4, we realize the algorithm in chapter 2 and chapter 3 by MATLAB programme. We use the SNTO method in Fang.K.T and Wang.Y.(1996) to compute the whole maximum and minimum value of the multiple functions. The convergence of SNTO is rapidly in our computation. In conclusion, the iteration algorithm and sequential generation in this paper is quite good for almost multiresponse model.