Likelihood-based optimization of threat operation timeline estimation

TerrAlert is a system that Metron, Inc. has developed to track the progress of suspected terrorist operations and optimize courses of action to delay or disrupt these operations. The underlying algorithms use Monte Carlo sampling and Bayesian, nonlinear filtering to estimate the state (schedule) of a terrorist operation defined by a project management model (such as a program evaluation and review technique (PERT) or Gantt chart) with uncertain task durations. However, in order to generate schedules via sampling, it is not sufficient to specify only the model and estimated task duration distributions. The analyst must also provide a distribution of start dates for the operation, which we have observed is relatively difficult for analysts to do accurately. In this paper, we describe a likelihood-based approach for estimating the most likely start date given the available evidence, and perform a series of experiments to validate this approach.