This research is concerned with inference on spatial stochastic processes. The two general problems considered are: (1) detect whether an observed, possibly incomplete realization of the process comes from a hypothesized probability measure; and (2) detect whether the underlying probability measure has changed from one realization to another. Crucial to our approach is the ability to simulate from the relevant classes of spatial stochastic processes.
In this research, we solve an applied-probability problem of relevance to the intelligence community. Understanding and quantifying the behavioral psychology of enemy nations under conflict situations (or perceived conflict situations) can lead to improved tactical counter-measures. A variety of important strategic questions can be answered that can provide extremely useful intelligence; for example, when threatened, does the enemy tend to retreat and defend, or aggressively counter-attack? Does the enemy attack in isolated pockets, or in a more uniform manner?
In this research, we look to answer these questions in specific situations where intelligence data give the positions and readiness-states of hostile mobile launcher systems. The affiliation and potential threat of mobile launcher systems can vary significantly under different readiness states. By smoothing the spatial point pattern of mobile launchers (at a given snapshot in time), we obtain intensity maps that quantify the potential threat the launchers imply.
Our interpretation and application of this has led to two approaches. The first is a global approach that models spatial locations of all detectable mobile launchers in a potentially hostile country at successive snapshots in time. The objective is to determine whether, and if so to what extent, the country is deploying positional changes in readiness to attack.
The second is a local approach. Here we characterize the country's readiness-state by the behavior of the mobile-launcher intensity at the same successive snapshots in time, but over selected regions of the country. The objective is the same as for the global problem.
Intelligence data is not generally good enough to track individual launcher locations through time, and hence the applied-probability problem we pose involves spatial point processes observed at different snapshots in time. As can be seen in the figure below, it may be difficult to detect differences between intensity functions generating the launcher locations by just viewing the observed launcher fields. When going from left to right in the figure, the true intensity functions for the fields involve launchers being shifted towards the northern and eastern regions of the country, representing low-, intermediate-, and high-threat situations. While it is clear from the figure that the high-threat situation in (c) is different than the other two, differentiating between (a) and (b) by eye is difficult. However, the difference between the first two fields can be described and detected through the use of summaries and hypothesis tests.
This research was supported by SPAWAR, San Diego
Last modified: Monday, December 10, 2007 11:55 AM.