Calculating POA

The POA is the probability that a given area actually contains the missing person. After it has been set initially it needs to be regularly updated based on changes; whether that is new evidence, or the area having been searched and nothing found. In this latter case the new values are calculated using Bayes theorem. Bayesian Search Theory has been in use for almost 50 years for locating items, initially for objects lost at sea (such as a missing hydrogen bomb lost off the coast of Spain and a missing US submarine, the Scorpion).[11]

Given that sensors are never perfect, it is almost always possible that despite

10 Chapter 2. Search and Rescue being searched an area still contains the missing person. This means that there are two possibilities — given that nothing was found, either the person wasn’t there, or they were. The prior probability that they were in that area (the previous POA) is known, as is the probability that they would be discovered if they were (POD), so the new POA can be worked out.[15]

Bayes theory states that

P (A | B) = P (B | A)P (A)

P (B) (2.3) For the area searched:

P (C | N ) = P (N | C)P (C)

P (N ) (2.4) where P (C) is the prior probability that the area contained the person (the previous POA), and P (N ) is the prior probability that the person wasn’t detected in the area. POD — the probability that the person would be detected given that they are in the area — would be P ( ¯N | C).

P OAnew=

(1 − P OD) × P OAold

P (N ) (2.5)

P (N ) = P (N | C)P (C) + P (N | ¯C)P ( ¯C) (2.6) P (N | ¯C) = 1 (2.7) P (N ) = (1 − P OD) × P OAold+ (1 − P OAold) (2.8)

P (N ) = 1 − P OD × P OAold (2.9)

P OAnew =

(1 − P OD) × P OAold

1 − P OD × P OAold

(2.10) The probabilities of all other areas need to be updated as well, to reflect the new information — showing that they are now comparatively more probable, now that a search elsewhere has proved fruitless.

2.2. Creating probability maps 11

P (Cx | NS) =

P (NS | Cx)P (Cx)

P (NS)

(2.11) where P (Cx) is the prior probability that area x contained the person (the previous

POA for that area), and P (NS) is the prior probability that the person wasn’t

detected in the area which has just been searched. P (NS | Cx), the probability

that the person wouldn’t be found in the area searched if they are actually in this different area, will logically be 1.

P OAx,new =

P OAx,old

P (NS)

(2.12) where P OAx,new is the new POA for the area x. It should be noted that this has

the same denominator as Equation 2.5 — the calculations required can therefore be simplified by not performing this normalisation step, as all relative probabilities will be unchanged. This means that, after a search, the areas not searched can retain their old POA and the searched area changes its POA to:

P OAnew= (1 − P OD) × P OAold (2.13)

Not normalising gives a number of advantages, including a reduction in the amount of processing required (only one area needs updating at a time rather than every area on the map), and an increase in the amount of useful information that can be obtained — if all areas are normalised (such that the POAs from all areas sum to 100%) then there is no way of knowing when the overall probability of the areas under consideration drops to such an extent that the missing person must be outside those areas. Either the search must be expanded, or the search suspended — there is no point in continually searching an area when it is unlikely that it contains the person.[11]

Note that calculating POA using the algorithms above may lead to a searched area that was found to not contain the person having a higher POA than an entirely unsearched area. This is logical — an area which is very likely to contain the person but which is very hard to search effectively is going to remain likely for a long time, while an area that is unlikely to begin with will remain unlikely, regardless of

12 Chapter 2. Search and Rescue whether or not it has been searched.

The creation of the initial land-based probability maps is covered in Section 2.2.2.2, after a brief description of marine probability map creation for comparison. 2.2.2.1 Sea

The location of an object lost at sea depends on several factors, but one of the most important ones is whether or not it is under human control. Ships which have failed to arrive may have left their predicted course at any point, and might have done so intentionally and under full control. The movement of a floating object, however, can to some extent be modelled mathematically. This is extremely useful, as in most cases an object requiring search and rescue will not be in control of their own movements; e.g. a life raft, floating away from a sinking ship.

A life raft (or similar floating object) will drift predominantly under environ- mental factors — wind, tides, current, etc.[11] — and the survivors themselves often have little or no control over their course by comparison. All of the main effects can therefore be calculated from known information, such as the weather, and informa- tion from systems available worldwide to accurately calculate currents.

Once the data has been collated a Monte Carlo simulation can be performed. Particles are placed at the last known position of the missing object, moved based on drift estimates, and their accumulated positions give a set of probabilities for where the actual object may be.[16]

Much more could be written on marine search and rescue, but it lies outside the scope of this thesis.

2.2.2.2 Land

There are various ways of defining land SAR areas. Koester[6], for example, splits them into wilderness, rural, suburban, urban, and water. In this thesis we are focussing on Wilderness, which is also referred to as Mountain, and to some extent on Rural. Goodrich et al.[17] describes wilderness search and rescue (WiSAR) as ‘finding and providing assistance to humans who are lost or injured in mountains, deserts, lakes, rivers, or other remote settings’. Koester describes Wilderness and

2.2. Creating probability maps 13 Rural respectively as ‘An area essentially undisturbed and uninhabited by humans. Although even in a wilderness area a network of trails and roads may be found’, and ‘An area relating to the countryside, marked by farming or raising livestock, which is sparsely populated. It is often mixed with open spaces and woods.’.

The search and rescue techniques required for this terrain are notably different from others. In Urban SAR,6 for example, any missing persons would be either inside the damaged building or they would be safe — and although some areas are likely to be more fruitful to search than others (for example bedrooms in a house late at night, or offices in an office building during the day), these decisions are based more on the types of area and less on the types of individual.

The probability map for a missing person on land is calculated from a range of information — including expert opinion from people who know the area, historical search statistics, and possible speed of travel over the terrain, amongst others.

On land a missing person’s movement is an unknown; they may move or they may stay still, and the direction, speed and distance are all based on a range of aspects which are hard to pin down — such as the person’s state, condition, age, etc. Fortunately some of this information can be obtained from statistics gathered from historical searches.

There is a large body of statistical knowledge available relating to land-based search and rescue, collated by organisations in many different countries. This infor- mation is split into missing person types. The large variation in behaviour of missing persons depending on their type is significant — a hiker will behave very differently to a child, or to someone who is suicidal, or to someone who has dementia — and the results for each person type as shown by each country are very similar.

The importance of this data is summed up by Perkins et al.[18]: ‘It is always useful to tell the search party prior to deployment how the missing person is likely to behave. How will they react to being the subject of a search? Will they try to hide, or to attract attention to themselves? If they went missing deliberately, how will they try to remain undetected? If they are lost unintentionally, how are

6_{‘Urban’, in this context, is being used to denote searching for missing people in buildings,}

usually after some form of disaster. In other contexts it can refer to people who are missing in a city

14 Chapter 2. Search and Rescue they likely to react, what actions will they take to remedy the situation?’ — the more information available to searchers, the better equipped they will be to find the missing person.

There are many organisations collating SAR statistics in different countries. In the UK both the Police and the Mountain Rescue Council of England and Wales produce statistics, and the latter releases regular reports — the latest of which was published in 2011.[19] Individual countries have only limited amounts of data to produce statistics from, however. One of the best methods for obtaining statistics, therefore, is to use the International Search and Rescue Incident Database (ISRID).7 ISRID was started in America in 2002 on the back of a research grant from the US Department of Agriculture, building on many previous sets of statistics,[6] and now contains data collated from more than 40 countries. By 2008 the database contained over 50,000 SAR incidents, and it is still growing.

The ISRID database first splits the missing person into a category (e.g. Child (with different categories for different ages), Hiker, Climber, Despondent — see Appendix B for a full list), and then further divides the statistics by area type (temperate, dry or urban). For this more specific scenario it provides a number of statistics, including probability of different distances found from initial point; elevation change (probabilities of the person moving up, down, or neither from the initial point); mobility in hours; dispersion angle (how far they are likely to spread from a straight line); common locations where found (e.g. by water, in woods, on roads, etc.); survivability (how likely they are to be found alive, for various lengths of time); distance travelled away from a track; and finally any other useful information (such as that people suffering from dementia will avoid crossing boundaries (roads, fences, etc.)).

Used properly, these statistics can provide the basis for a probability map. It is important to note, however, that these statistics don’t mean that all similar sit- uations will be exactly the same — they’re just a good place to start, and making too many assumptions can be dangerous. As Koester[6] said, ‘The most dangerous planner is one who has seen a situation once or twice and tends to think all future

7

Into which both the Police and MREW submit data, along with similar organisations in many other countries

2.2. Creating probability maps 15 subject behavior will be just like the last one’.

One of the most useful statistics is the distance at which the missing person is usually found. This allows a series of concentric circles to be plotted on a map, showing the differing levels of probability that the person is within each circle. This is known as the Bicycle Wheel Method. A missing person is most likely to be found within the ‘hub’ of the wheel. They are almost certain to be found in the area covered by the entire wheel, although that may be a very long distance from the hub. Radially out from the centre of the wheel are ‘spokes’ — natural pathways that the missing person may have followed. Depending on the other statistics, the search teams will probably want to concentrate initially on these paths within the ‘hub’, then fill in the areas between them, and then repeat for the remainder of the wheel.

It should be noted that statistics do not alone make up a new probability map. A lot of weight is given to the opinions of experts, who come up with a variety of scenarios for what might have happened to the missing person based on the available evidence. These scenarios are likely to be based on the statistics, but may entirely disregard some as not being applicable or important. The opinions of many experts can be collected, and an average weighting for each search area obtained using a Mattson Consensus. It is these opinions which create the probability maps, but it is the statistics (along with personal experience of the area and any unusual factors, such as the weather) which inform their opinions.

2.2.2.3 Criticism

Marine search and rescue has taken classical search theory into account for a long time, but land-based search for missing persons has in the past lagged behind some- what. The probabilities for land-based SAR are affected by a wide range of sources and their calculations have often been misunderstood by researchers, leading to many people conducting plausible but ultimately incorrect studies in this field.

Because of this, the US Department of Homeland Security and US Coastguard commissioned a review of land-based search strategy due to the lack of ‘a compre- hensive attempt to apply the science of search theory to the development of land

16 Chapter 2. Search and Rescue search planning and techniques’.[11] Published at the end of December 2003, this extensively reviewed previous methodology and provided a framework for the areas requiring research. Although this and similar papers produced much controversy at the time,[20] since that point there has been much work carried out to bring land-based searches in line with search theory. This history of improper research, however, has marred the opinion of some groups of current land search theory.

In mid 2009, as part of the research for this thesis, some questions were put to Mark Harrison (at the time the National Police Search Advisor). Regarding the body of research produced internationally by volunteer organisations, he questioned the relevance and reliability of their datasets — in particular, the use of data from other countries for searches in the UK — and hence the validity of the conclusions that can be drawn from their work. The UK police have conducted extensive (unpublished) research into their own data, profiling by behaviour instead of by activity. This research is used by the police both when searching for missing persons and when searching for criminals.

Despite such criticism, the historical data used by volunteer groups around the world (profiling by activity) is in everyday use[6] and there is much research based around it. The ISRID database does include some data provided by the British police;[21] similarly, if the use of international statistics was problematic, the statis- tics from Mountain Rescue (England and Wales) are also available.[19]