Donald Bamber

It is an understatement that both the theory and applications of probability conditional or unconditional play an essential role in the processing and use of disparate information in decision-making in C4I systems. Apropos to the theme of this symposium, Making Information Superiority Happen, the paper outlined here describes new applications, insights, and theoretical aspects of ongoing work by the authors toward improving the rationale for use of probability theory, keeping in mind issues of scalability and computational complexity. This paper extends the ideas first presented in last year's CCRTS at Newport, RI. In short, the mathematical theme of this paper is both a summary of past research efforts together with new results on the problem of best estimating partially specified conditional and unconditional probabilities of interest via a second order bayesian probability approach. Among the new derivations provided in this paper is a significant reduction in computational effort in obtaining (again, in the second order probability sense) optimal or near-optimal probability estimates, all within the setting of a boolean conditional event algebra which allows full compatibility with conditional probability evaluations.