TECHNOLOGICAL DATA ANALYSIS USING THE METHOD OF TESTED PRIORS

The 'Method of Tested Priors' utilizes the subjective information of an experimenter, given in the format of an initial estimate of the parameter vector. On the basis of this estimate, a region R, called 'the benefit of doubt region' is constructed. Full scale prior distribution is kept out. A sample of size n(,1) is taken and if the sample mean falls within the region R, the parameter is estimated by a function of the initial estimate and the sample mean. Otherwise a second sample of size n(,2) is drawn and the mean is estimated by the weighted average of the two sample means. The merit of this procedure is evaluated by comparing the mean square error of this estimator with that of the estimate using the classical procedure with the equivalent sample size.

The above scheme was modified within the two stage structure. It was also extended to sequential procedures. One major modification was to incorporate the prior variance in the estimation scheme. In this case the region R is a function of the prior variance, and if the first sample mean is in the region R, the mean is estimated by the weighted average of the initial estimate and the sample mean, the weights being proportional to the reciprocal of the corresponding variances.

Properties of the estimators are derived for univariate as well as multivariate normal distributions, and the efficiency is tabulated for all the cases we studied. To verify the accuracy of the mathematical derivations, the efficiency is simulated using Monte-Carlo techniques. The simulation results were in close agreement with the theoretical results.

The philosophical basis for the development of this estimation scheme is explained in chapter I, and is constantly used as the basic vehicle for formulating and modifying the procedures.