Determining causality of an adverse drug reaction (ADR) requires a multifactor assessment. The classic Naranjo algorithm is still the dominant assessment tool used to determine causality. But, in spite of its effectiveness, the Naranjo algorithm is manually intensive and impractical for assessing very many ADRs and drug combinations. Thus, over the years, many "automated" algorithms have been developed in an attempt to determine causality. By-and-large, these algorithms are either regression-based or Bayesian. In general, the automatic algorithms have several major drawbacks that preclude fully automated causality assessment. Therefore, signal detection (or causality screening) plays a role in a "first pass" of large ADR databases to limit the number of ADR/drug combinations a skilled human further assesses. In this work a Bayesian signal detector based on analytic combinatorics is developed from a point of view commonly adopted by engineers in the field of radar and sonar signal processing. The algorithm developed herein addresses the commonly encountered issues of misreported data and unreported data. In the framework of signal processing, misreported ADRs are identified as "clutter" (unwanted data) and unreported ADRs are identified as "missed detections". Including the aforementioned parameters provides a more complete probabilistic description of ADR data.