By Chris Nichols
The recent Pleasant Hill search provided a simple example of working with Bayesian statistics to quickly find a subject. An efficient search is a balancing act between accurate field information and the allocation of resources by search management. The interplay between the two is one of the many activities that distinguish the lay searcher from the professional searcher.
For starters, the professional searcher thinks in terms of defined areas. This allows search management to better manage operations.
Another aspect is that the lay searcher is looking for the subject, while the professional searcher is also looking for clues and, almost as important, finding areas of where the subject is not.
Finally, one of the largest differences between lay and professional searchers is that the professional searcher thinks in terms of probabilities. Where a lay searcher might clear a trail and determine the subject is not there, the professional searcher might conclude that there is a 50 percent probability that the subject isn’t there. While the difference might seem slight, the practical application is huge.
Using the Pleasant Hill search as an example to pull this together, our team was on scene two hours after the subject went missing, allowing us a limited search area. Because of the behavior of the subject, we narrowed down the high probability areas to two segments. Search management now had a path to manage field teams. However, we still didn’t know if the subject would go north or south – this is where Bayesian statistics came in.
Since the subject could have turned left or right equally, we divided Contra Costa Blvd. into two segments, one south (Segment A) and one north (B), each having a 50-percent probability. We sent the first team south. Let’s say they came back with a probability of detection of 30 percent. We now can work the math so that our new probability of area (POA) equals (1-30 percent) X 50 percent / 1-(50 percent X 30 percent), or 41 percent.
Since the probability of area A goes down, that means the probability of area B goes up even though it has not been searched yet (a 0 percent of probability of detection). This can be proven in the formula 50 percent / 1-(50 percent x 30 percent), or 59 percent. Thus, Segment A’s POA went down from 50 percent to 41 percent after the first team completed its assignment, while B’s went from 50 percent to 59 percent.
We now can put additional resources into B (which we did) to bring down the probability. The inclusion of our old probability of area of 50 percent is what makes this a “Bayesian” calculation, after mathematician Thomas Bayes came up with theory in the 18th century. The inclusion of our old probability in the calculation serves to “anchor” our estimation closer to reality vs. other statistical methods.
After picking up some clues in the Pleasant Hill search, we started to flood the area with searchers in Segment B where the subject was eventually found. This mission provided us with the most basic example imaginable. Adding more segments would have complicated things fast, as we would have recomputed the POA for each segment searched and not searched. If we have 25 segments, as we often do, that is 25 x 25, or 625 computations per debrief. This is one reason why we keep a set of laptops handy in the CP.
Most important, the above calculations are mathematical proof that field teams are effective even when they don’t find the subject. Knowing that we have a reduced probability of Segment A allows a higher probability of success for the team searching B. If taken to the extreme, we could end up with the statistical probability in the final unsearched segment of something approaching 100 percent.
While a team injected to that final area would surely make the find, the mathematical reality is that the team searching that segment did comparatively little, as it was only through the effort of all the other teams in all the other segments that pointed the search manager to put that team in the final segment. This is why search and rescue is truly a team effort.
Next to staying safe, accurately assessing your probability of detection so the above analysis can be as precise as possible is one of the most important items you can do. No matter what your experience, having knowledge of how resources are allocated will not only help you better understand the search process, but will improve your capabilities as a professional searcher.