Final Report for the Project “Robust Rapid Change-Point Detection in Multi-Sensor Data Fusion and Behavior Research” (FA9550-08-1-0376)

It is well known that quantization cannot increase the Kullback-Leibler divergence which can be thought of as the first moment of the log-likelihood ratios. In this paper, this result is extended to the case of second and higher moments of the log-likelihood ratios. It is shown that quantization may result in an increase of the second or higher moments of the log-likelihood ratio, but such an increase is at most by a universal constant that only depends on the value of the moment. Such a constant is 2/e for the second moment. The result is further applied to decentralized quickest detection problems to provide a simpler sufficient condition for the asymptotic optimality theory.