## President's Letter

Metron's work carries an underlying theme. It is the application of mathematical models to the solution of real world problems, particularly those related to national security. This work requires skill, discipline, and faith in mathematics. The act of faith involves creating a mathematical model of a system or process and expecting it to provide the basis for sound decision making and insight.

Mathematical models are by necessity simplifications of reality. It is amazing how often and how well these models work. The effectiveness of mathematics in modeling the real world has been noted and discussed by many scientists, in particular by Eugene Wigner, in "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," in Communications in Pure and Applied Mathematics, Vol. 13, No. I. We are so used to this phenomenon that we take it for granted. Nonetheless, it is supremely rewarding when a mathematical model you have developed provides good guidance for making decisions or insight into the operation of a complex system.

Metron applies Bayesian inference to problems and systems involving uncertainty. In Bayesian inference, uncertainty is modeled by probability distributions. Observations about the system are converted to likelihood functions which are used to compute posterior probability distributions on the state of the system. This posterior distribution reflects the way the observation has modified, and hopefully decreased, the uncertainty in our knowledge of the state of the system. This process involves a simple concept called Bayes' Theorem enunciated by the Reverend Thomas Bayes in his "Essay towards solving a problem in the doctrine of chances" published posthumously in the Philosophical Transactions of the Royal Society of London in 1764. In spite of its simplicity, Bayesian inference has been highly effective when applied to solving complex problems in detection and tracking involving low signal-to-noise ratios and high false alarm rates.

In these days of powerful, inexpensive computers with wonderful graphics capabilities, our mathematics and models live in software. We can display the results of our computations in graphical representations that allow a user to understand and act on our results without having to comprehend the intricacies of the models themselves. Obviously, mathematical skill and talent are required to develop and implement these models. Beyond those requirements, one needs the discipline to stick to a coherent model of the problem being addressed. All too often people succumb to the temptation of applying a quick, ad hoc fix to a model to make it "behave" properly. This may solve the short-term problem, but it corrupts the model and dilutes the insight and applicability of the model. In our experience, a well-constructed coherent model performs better than a corrupted one.

It is the adherence to coherent models and sound mathematical reasoning that is at the core of Metron's philosophy of work. This distinguishes Metron from other companies that work on similar problems and is what makes Metron an exceptional place to work.