Posts Tagged ‘Theory of Optimal Search’

Calculating Probability Density Distribution for Missing Person Search

January 26th, 2010

The first of the four elements of the optimal search problem is having a probability density distribution (predicting the likelihood that an object is in any particular search area or region.)

To achieve this during a Maritime Search and Rescue Incident one takes into account the accuracy of the initial location report, the current, wind and so on. Computer models can then accurately map the likelihood of the boat (or whatever search object is being sought) being in any particular area.

However, the variables for a vulnerable missing person search are not yet known with any particular accuracy. They may choose any direction; may stay on paths or tracks, or depart from them; camp or find shelter; try to cross rivers; go uphill or down; and so on and so on.

Computer models of missing person behaviour then are not as useful or accurate as Maritime models. This does not, however, mean that we cannot come up with useful probability density distributions. Take a quick glance at Robert Koester’s, Lost Person Behavior book to see that the world SAR community has over 50,000 incidents’ data to draw upon.

From this we can predict the likelihood a given misper will travel a certain distance from their initial location and misper “type” or “category”. This is sufficient to draw a couple of circles on a map and calculate probability density’s for concentric regions on a map. It is a small step from this to calculate actual Probability of Areas (POAs) for specific search sectors.

Other potential methods for calculating probability density distributions include the consensus method – allowing for subjective calculation based upon search planners’ experience, the individual misper intelligence and the actual search terrain limitations.

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Elements of the Optimal Search Problem

January 19th, 2010

Lawrence Stone defined the elements of the optimal search problem in his 1986 book, Theory of Optimal Search.

This was paraphrased extremely well by Cooper, Frost and Robe in their 2003 report – Compatibility of Land SAR Procedures with Search Theory as quoted below;

A probability density distribution on search object location and state (so the probability of containment, POC (a.k.a. POA for “probability of area”), for any subset of the possible locations and states can be estimated),

A detection function relating the probability of detecting (POD) the object if it is in a searched area to the density of the searching effort expended there,

A known finite amount of available searching effort, and

An optimization criterion of maximizing probability of finding the object in a desirable state (probability of success or POS) subject to the constraint on effort availability.

I will endeavour to simplify further. In order to need and/or use the mathematics of search theory you require four essential elements.

  1. The ability to predict the likelihood that an object is in any particular search area or region. This might be done using sophisticated computer software working with the latest missing person behaviour statistics, or could be as simple as a coming up with a consensus within the search planning team.
  2. The ability to calculate the likelihood a given search resource will have of finding the object if it in the area being searched – unfortunately we can’t ask how many clues would you have found! [See my definition of POD for a brief explanation of why]
  3. A limited but known amount of search resource – when do you ever get too much search resource?
  4. A method of calculating the best way to use the search resource to maximise the chances of finding the search object as quickly as possible.

I’ll look in detail at each of these in further posts.

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