Threat detection (TD) means an assessment of the presence of harmful agents, biological, chemical, or nuclear. The footprint (or signatures) of such agents could be qualitative and verbal, and/or quantitative. These signatures are generated by sensors which collectively form a networked system. The architecture of such systems could be series, parallel, or hierarchical. A key feature of such signatures is that they tend to be imprecise, incomplete, and unreliable. Furthermore, the sensors could be co-operative or adversarial, the latter due to sabotage and psychological ploys. The principal investigator and his colleagues propose to articulate the mathematical underpinnings of the TD scenario, in order to integrate signatures from a multitude of sensors in a principled way. The goal is to express the presence of threats in terms of numerical probabilities. This tantamounts to integrating signatures which are filtered via distributed network structures, and are contaminated by imprecision, camouflage, and parleying. As a research topic in probability and statistics, the matter of integrating contaminated and camouflaged signatures is new. Both Bayesian and classical methods, as well as a cunning combination of the two, will be invoked. The crux of the work will entail developing meaningful likelihood functions that capture the essence of the physical and psychological issues.
Current practice in intelligence and national security is to express threat in verbal and qualitative terms like possible, probable, likely, etc. Such expressions are not actionable. This research will place the threat detection scenario in a probabilistic framework so that decisive actions to mitigate threats can be taken. The work will have broader impacts in civilian applications such as oil exploration, weather prediction, medical diagnosis, and socio-cultural modeling.
The research performed here is by a team of 6 investigators with a broad spectrum of skills in the mathematical sciences; it covers a period of four years. The driving theme of this work pertains to diagnostics (the mathematics of medical diagnosis, threat detection, and target identifcation). It has resulted in 22 reports and publications, literally all of them in peer reviewed outlets, and numerous presentations, national and international. It has also created a small cadre of new investigators in an arena that is relevant to human well being and national security. Besides several methodological and conceptual developments in probability and statistics which constitute the intellectual merits of this work, and which are encapsulated in the published outlets, the research successfully adresses a long standing problem in diagnosis, namely, developing an omnibus measure for assessing the efficacy of diagnostic instruments. Its roader impact covers a range of disciplines, such as signal processing and target identification (via approaches for fusing information from several sources), econometrics (via new measures of wealth concentration and inequalities), physics, biology, and chemistry (via a general algorithm for solving an archetypal system of equations that these disciplines spawn), source selection (via a model for percolation across hierarchies), and the defence sciences (via an algorithm for logistics and routing over networks laden with obstacles like cyber attacks and IED's). The prospect of patenting and commercializing aspects of this work look promosing and vehicles for doing so are being explored. The project has also contributed to the development of a new cadre of individuals ( a post doc and a doctoral student) who can continue on the pathway that the project has created, and in so doing add to the scientific pool of researchers whose skills would be germane to medical diagnosis, national security, defense, geospatial imaging, and issues ipertaining to the treatment of uncertainties in the basic sciences such as physics, biology, chemistry, and nuclear science.
