A Comparison of Bayesian and Information-Optimal Detector Thresholds

The binary inference procedure including the experiment and detector is viewed as an "inference channel" transmitting information from event to decision. In this formulation, the mutual information of event and decision is used to measure the performance of the entire inference channel. Maximizing the mutual information requires optimizing three components of the inference channel, the experiment, the test statistic, and the threshold comparator. It is shown that the information-optimal test statistic is the likelihood ratio, and a method of choosing the information-optimal threshold is demonstrated both with and without knowledge of the prior probabilities. The relationship between Bayesian and information-optimal thresholds is explored.