Predicting ROC curves for source detection under model mismatch

Performance predictions and test thresholds for the task of detecting a gamma-ray source in background with a position-sensitive detector are often costly to compute empirically. The asymptotic distributions of test statistics for detecting a point-source in background give reasonable performance predictions in terms of the receiver operating characteristic curve (ROC) with less simulated or measured data than empirical methods. The asymptotic distributions also allow the user to determine the proper threshold to achieve a desired false alarm rate. Typically only approximate models are available or practical for complex gamma-ray imaging systems such as 3D position-sensitive semiconductor detectors. Applying standard formulas for the asymptotic distributions of maximum likelihood (ML) estimates in the presence of model mismatch can yield inaccurate and sometimes overly optimistic predictions of detection performance. We apply the theory of the asymptotic distribution of ML estimates under model mismatch to the case of detecting a point-source in background with a 3D position-sensitive CdZn Te detector employing an approximate model for the system response. We show that performance predictions computed using an asymptotic approximation that accounts for mismatch more closely match the empirical performance than predictions generated by an asymptotic approximation that ignores model mismatch.