Setting Limits, Computing Intervals, and Detection

This article discusses a number of statistical aspects of source detection, thecomputation of intervals and upper limits for a source intensity, and accessingthe sensitivity of a detection procedure. Emphasis is placed on model diag-nostics, validation, and improvement as means of avoiding odd behaviors in theseprocedures such as over abundant short or empty intervals. Improved modelspecification is viewed as a better response to systematic uncertainties, thelook elsewhere effect, and general model inadequacy than simply insisting on asignificance level of 5σ for source detection. We advocate reporting both theupper limit and the sensitivity to better represent the strength of evidence fordetection and the reported source intensity. Finally, we explore the use ofdecision theoretic analysis to derive detection procedures, intervals, andlimits in order to focus attention on the statistical properties of primaryinterest.