Probability-Weighted D-Optimal Designs Considering the Distribution of the Factors

The prior distribution information of the factor is usually available, but it is ignored by the standard optimal design. For the sake of considering the distribution information of the factors in an optimal experimental design, the following works are done: Firstly, the least expected squares estimator (abbreviated as ELSE), which can consider the distribution information of the factors, is defined. Secondly, based on ELSE, the probability-weighted D-optimal design is developed, and the relevant concepts, such as information matrix, D-optimal criterion and D-efficiency are redefined. Thirdly, the relevant theorem and algorithm for the construction of the probability-weighted D-optimal design is discussed. Lastly, examples are given to show that the support points of the new design are more concentrative around the area with higher probability density, which is more consistent to the common sense.