Methods

We are using a Bayesian network framework for our models of lost-person behavior. Bayes' theorem is already familiar to search managers. It is simply the proper way to update degrees of belief given new evidence, and has already been incorporated into CASIE III, Koopman's search theory, the U.S. Coast Guard's CASP software, etc. A Bayesian network is an efficient way to encode uncertain knowledge in a way which allows proper reasoning under that uncertainty.

However, so far as I am aware, models of lost person behavior have used traditional statistics (multiple regression, etc) for generating estimates, rather than path analysis or other forms of causal modeling. If we first construct a diagram with arrows representing causal links between variables, and omitting links between variables which cannot directly influence each other, then the techniques of path analysis allow us to decompose the regression coefficients into the appropriate weights on each link in the model. Consequently, once we have those weights, our predictions will be more accurate, since they more accurately capture the causal structure. (Of course, this all assumes we can get the proper model, but that's part of what we are testing.)

A Bayesian network is a generalization of path analysis: it allows nonlinear functions between nodes in the network, and provides a very efficient way to represent and reason with uncertain knowledge. Bayes nets underlie the most successful expert systems used in medical diagnosis.

We are testing networks made both by experienced search managers, and those found by machine-learning algorithms. Our machine-learners use Minimum Message-Length (MML) Inference. Based solidly in information theory and Bayesian inference, MML is basically the information-theoretic interpretation of Ockham's Razor: it strongly (and correctly) penalizes more complex hypotheses, and thus does not overfit the data.

Our methods for Optimal Resource Allocation come from the literature on search theory, usually known as operations research. Given an initial probability map and a technical measure of the effectiveness of each resource in each area, there are algorithms which far surpass anything currently used in land search (e.g. CASIE-III). We have designed SORAL to be a standard package which handles all of the mathematics so you don't have to spend the time we just did. For more details see the SORAL project documentation.

Background

As far as I know, the statistical study of Search & Rescue was pioneered by Dennis Kelley in his 1973, Mountain Search for the Lost Victim, available from the author, and by William G. Syrotuck in his 1975 An Introduction to Land Search Probabilities and Calculations and his 1976 Analysis of Lost Person Behavior, now both available in updated form from NASAR.

The theory of optimal search was first developed by B.O. Koopman, Search and Screening. A simplified and very accessible text The Theory of Search by Jack Frost is available in Microsoft Word format from Martin Colwell's SAR library. That work explains primarily maritime search planning. Also available on Martin's site is Principles of Search Theory that appeared in Response and is much more attuned to land SAR. Paper reprints of both are available from NASAR at a nominal fee to help cover production costs. Another introductory text available for about US$12 is Search and Detection by Alan Washburn, now in its third edition.

More locally, and long in advance of my interest, Rik Head Emergency Systems Technology Pty., Ltd. had constructed his own systems model of subject mobility and survivability in a non-Bayesian framework, and implemented it in a computer program ("Search System") for assisting search managers. We will be looking at extending or incorporating that model into SARBayes.

Technology

One task is to investigate whether the classical categories of lost persons provide a good explanation for the existing U.S. and incoming Australian data. We use the MML-based classification program Snob to discover the natural classes in the lost-person data.

We will also use MML to infer the most parsimonious causal models, and compare them to expert-specified models using CaMML: Causal Modeling with MML, as it consistently outperforms the more well-known programs like TETRAD.

In our front-end program, the underlying represenation of the Bayesian networks is handled by Netica, a package with a good programmer's API on Windows, Mac, and Linux, and a nice GUI for Windows.