Unified framework for performance analysis of Bayesian inference
Many problems in image analysis and ATR can be formulated as Bayesian inference. In this paper we present a unified framework to quantify performance (i.e. the accuracy and uncertainty of inference) in terms of Bayesian decision theory. We demonstrate that existing work on image analysis and ATR performance can be summarized in terms of these concepts. This includes performance measures such as signal- to-noise ratios, Cramer-Rao lower bounds, Hilbert-Schmidt bounds, and ROC curves. Secondly, we describe how recent work by the authors on order parameters can be reformulated within this framework. This includes analyzing how phase transitions can occur for target detection problems so that at critical values of the order parameters it becomes impossible to detect the target. We also analyze the case where the inference process uses weaker prior knowledge to detect the target and quantify in what situations this strategy is effective.