Spreading probability around

A couple of 3D wireframe images comparing "raw" probability profiles to "pden" profiles.

In the wireframe images above, the left-hand image shows the "raw" distribution. The right hand shows the probability density -- the effect of taking the area of the ring into account. A dramatic illustration of why we should search close in first, other things being equal.

Discussion

We're used to histograms showing how far lost people travel, on average, for different classes. For example, the following histogram from the NATSAR report.

Of course, we know that to apply this to a search, we have to spread that distance out over the 2D surface. Ideally, we take terrain and vegetation into account, but usually we settle for "probability rings". For his upcoming book giving the statistical summaries of the very large ISRID database, Bob Koester asked me to make some plots showing how probability spreads out over space.

Paul Harrison helped me with the PyLab code for wireframes that rotate the distance distribution about the origin.

I cut off the data at 95%, and divide it into 5 bins. For Hikers in the ISRID database, that works out to:

95% range: 12km
bins (km):  [1.2, 3.6, 6.0, 8.4, 10.8]
# hikers :  [ 55,  30,  17,   8,    3]
% hikers :  [49%, 26%, 15%,  7%,   3%]
area(km2):  [ 18,  54,  90, 127,  162]

Notes:

Bob's book: Lost Person Behavior: A search and rescue guide on where to look - for land, air, and water. Due out about May 2008.

Note: Last summer, Martin Colwell showed me similar graphs that he presented at the NASAR conference and elsewhere, to make the same point.

Note: The data is not quite right. Better versions in the next entry .