by John Bownds, Michael Ebersole, David Lovelock and Daniel O'Connor
Copyright ©1994.
Section IV
1) the potential effect of the clue must be judged, and We will then provide a method for arriving at the numerical influences a clue has on an existing Probability of Area (POA) distribution. It will be seen that all of the numerical work - formulas, calculations, and bookkeeping - are handled automatically by the newest version of the CASIE software. This will make it possible to use subjective clue information in a manner similar to the way information on Probability of Detection (POD) is used to update the POAs after a search area segment is searched. Assuming the search management is following the basic procedures described in the standard "Managing the Search Function" (MSF) or similar courses, the initial POA distribution should change ("shift") as the search progresses, to reflect relevant information gained from perhaps a variety of sources. The method for updating the POAs uses Bayes' formula, a requirement so that all the input information remains consistent with the original POA distribution. Historically, the POA updating was developed primarily for use when a search segment was covered by a resource with a given POD, resulting in negative results (no find). The idea of updating the distribution when the search produced some potentially positive information (a clue) has always been attractive mathematically. Unfortunately, a practical method for doing this has been elusive. As a result, there have been no systematic procedures for evaluating a clue in the MSF or similar course. This article offers a systematic approach, including a specific version of Bayes' formula for use in computing the POA updates. We have developed the method in such a way as to be consistent with the underlying probability theory. Equally important, however, we have tried to base the approach on what we believe to be a sound, common sense application of search theory. No mathematical details are described here in favor of a more descriptive presentation. We emphasize that the method below requires several subjective estimates from search management. In the most recent release of the Computer Aided Search Information Exchange (CASIE) software, all of the necessary calculations are done automatically. We only require the computer operator to follow the appropriate menus and input the search management's subjective assessments. It is possible to perform the calculations below manually, but many difficulties are avoided by taking advantage of CASIE, which is public domain software. Two main questions arise in trying to construct a "mathematized" evaluation of general search information for use with a computer based management aide such as CASIE: 1) Should practically any kind of information be processed for updating the POAs? (That is, is there a limit to the type of search information we should attempt to process?), and 2) Exactly how should very subjective information be converted into mathematics for use in a computer, while keeping the methodology as scientifically rigorous as possible?
In the interest of using the widest possible interpretation of potentially useful information, we will define a clue as any information, in any form, which, in the judgment of the search management, may reasonably relate to the whereabouts of the missing subject.
We evaluate a clue in two stages. In the first stage, we estimate the potential influence of the clue on every search segment, including the Rest of the World (ROW). This simply means a judgment must be made whether the clue suggests the missing subject is in, or not in, each search segment. In doing this, we assume the clue is very likely authentic and so it is the potential influence of the clue that is the issue at this first stage. The matter of authenticity is covered later at the second stage. To accomplish the clue evaluation, the search management assigns a letter (A through I) to each search segment based on the information in Table 5. We want to emphasize again that we are evaluating the potential influence of the clue based on an initial assumption that the clue is very likely authentic.
With this approach, each letter chosen will be eventually converted to a certain percentage to be given below. Again, it is important to remember that the choices made in Table 5 are based on the assumption that there is no question of the clue's authenticity; it is authentic for the purposes of Table 5. We will use the following example to show how we can evaluate a clue. Suppose a search area is divided into four segments having POAs: Segment 1 = 40%, Segment 2 = 30%, Segment 3 = 20%, Segment 4 = ROW = 10%. If we are confronted with a clue, we take the first step, which is to evaluate each segment using Table 5. (At this stage we do not question the clue's authenticity). Suppose we decide that the clue's potential influence on each segment is:
Segment 1 = A (Clue strongly suggests subject in this segment), Our intuition suggests the POA for Segment 1 should remain the highest and the POA for the ROW should remain the lowest. The POA for Segments 2 and 3 should be adjusted in such a way as to be consistent with the original POAs and the clue evaluation. The question is: How much should each POA change? Our choices will effectively change all the POAs in a way we can eventually determine. But, at this point, we must now consider the clue's authenticity. Clue Authenticity The second stage in evaluating a clue involves its authenticity. In Table 5, a clue's potential influence is estimated using any of nine choices (A through I). In Table 6 we have restricted the clue's authenticity rating to five choices. It is our view that more resolution (greater than five choices) is neither realistic nor really needed. We rate the clue's authenticity using Table 6, based on the definition: A clue is authentic if it originates from a reliable source and it is clearly related in an important way to the missing subject. We make no attempt to define "reliable" or "related in an important way." We believe these terms are best interpreted on a case-by-case basis by the appropriate search management.
Numerical Clue Influence Table To effect a change (or "shift") in the POA distribution, we must resort to some calculations. Fortunately, all of this kind of labor can be left to the computer because the latest version of the CASIE software will perform all the calculations and bookkeeping. This program will convert the choices we make in Table 5 and 6 into an updated POA distribution, similar to the way it processes Probability of Detection (POD) information after a search. Simply put, this means that once we complete our two-stage clue evaluation by using the above tables, we can use CASIE to determine the new POAs in order to plan our response (if any) to the clue. For the purposes of field applications, the numerical table we supply below need not even be mentioned if CASIE is going to be used. However, for the purposes of understanding how the clue evaluation process alters the POAs, and for a more complete presentation, we outline the procedure here. With the potential influence of the clue evaluated for each segment using Table 5, and with the clue's authenticity rated using Table 6, it is now possible to determine the numerical influences of the clue (IOCs) from Table 7. Here is how we find the IOCs: 1) For each search area segment, we take the Potential Influence Level we have selected from Table 5 and enter Table 7 from the top; 2) We take the Clue Authenticity Rating we have selected from Table 6 and enter Table 7 from the left. The numerical influence of the clue is found where influence and authenticity meet in the table. Remember, the IOC for each search area segment (including ROW) must be found in Table 7, and the authenticity rating must be the SAME for all area segments.
(Entries are percents)
Continuing the previous example, recall that the clue resulted in the following potential influence levels: Segment 1 = A, Segment 2 = G, Segment 3 = C, Segment 4(ROW) = I. Now, depending on the clue's authenticity rating, the numerical IOCs are found from Table 7 as follows:
If the clue rating is very likely authentic, then: With the IOCs having been determined from Table 7, we are now ready to perform the necessary calculations for updating the original POAs. We provide this formula in the next section. First, however, by way of providing some rationale behind the IOCs in Table 7, we will list the main properties used to derive the table. We view these properties as fundamental to the underlying search theory. It can be shown that the following properties actually imply the numbers appearing in Table 7:
When these properties are used with the Bayes' formula, it can be shown that the entries in Table 7 are uniquely determined and are consistent with basic requirements in the underlying probability theory. No further details, beyond demonstrating the actual formula, will be given here in the interests of brevity and space.
Given the IOCs, found from Table 7, we can now update the original POAs and thus see the "bottom line" on what effect the clue has actually had on our calculations. For purposes of describing the required Bayes' formula, let's use S1(old) to denote the original POA of Segment 1, S2(old) the original POA for Segment 2, and so on with SN(old) denoting the original POA of the last (Nth) segment. We will use the last segment, Segment N, to denote the ROW. The updated POAs will be denoted by S1(new) for Segment 1, S2(new) for Segment 2, and so on. With this, we calculate the POAs, updated with the influence of the clue (and its authenticity rating), as follows:
Let D = S1(old)*IOC(1)+S2(old)*IOC(2)+...+SN(old)*IOC(N). Continuing the above example, setting the original POAs as S1(old) = 40%, S2(old) = 30%, S3(old) = 20%, S4(old) = 10%, the updates are calculated using the formula. The results depend on the authenticity rating as we see in the following table.
One property used in developing the IOCs table (Table 7) is that the entire clue evaluation process must be reversible; we listed this property as item 4 above. That is, we need the ability to "cancel" the updated POAs if the clue is later found invalid in some sense. For example, perhaps the source of the clue is later found very unreliable and we wish to "undo" all of the effects of the clue. The procedure we use for reversing the effects of a clue is simply to apply the "complement" of the bad clue to the current POA distribution. That is, any search segment assigned a potential influence of "A" is now assigned "I". Similarly, "H" is used in place "B," "G" in place of "C," "F" in place of "D", and "E" is used in any segment previously assigned "E" with the bad clue. The authenticity rating must be the same as that made originally when the clue was thought to be valid. In the above example, the potential influences of the clue were Segment 1 = A, Segment 2 = G, Segment 3= C, Segment 4(ROW) = I. To negate the clue, we apply the complementary influences Segment 1 = I, Segment 2 = C, Segment 3 = G, Segment 4= A. According to the results in the example, if the clue was assumed Likely Authentic, the updated POAs were found to be as follows:
Segment 2: 10.6%, Segment 3: 20.0%, Segment 4(ROW): 2.1%.
Segment 2 = 30%, Segment 3 = 20%, Segment 4(ROW) = 10%. We note here again that the CASIE software can perform all of our required calculations so that a search management team need only concern itself with clue evaluation judgments and not be bothered with Bayes' formula and the associated mathematics.
Since the task of determining the initial POA distribution (i.e., Mattson or O'Connor POAs) frequently (if not always) amounts to subjective choices and decisions by search management, the above clue evaluation method can be of assistance at the very first stage of a search. For example, suppose there are three search segments (plus the ROW), and the point last seen (PLS) is in Segment 1 and the direction of travel (DOT) is from Segment 1 to Segment 2 to ROW. These two pieces of information (PLS and DOT) serve as two clues. If the initial POAs, with NO information at all, are assumed equal, then we might start with Segment 1 = Segment 2 = Segment 3 = Segment 4(ROW) = 25%. We may then process the clues just as we have described above. More specifically, we consider each clue separately: Clue #1 (PLS): Assume the search management chooses the potential influences of the PLS clue to be Segment 1 = A, Segment 2 = A, Segment 3 = A, Segment 4 (ROW) = I using Table 5. Assume the authenticity rating for this clue is chosen from Table 6 as Even. This information could be used with CASIE, which would then supply the first POA update. If it were necessary to update using manual calculations, then we would refer to Table 7 and obtain the numerical IOCs as IOC(1) = 100%, IOC(2) = 100%, IOC(3) = 100%, IOC(4)(ROW) = 25%. The first update of the POAs is then computed from Bayes' formula with the result:
Clue #2 (DOT): Assume the search management chooses the potential influences of the DOT clue to be Segment 1 = B, Segment 2 = A, Segment 3 = I, Segment 4 (ROW) = D. If the authenticity rating for this clue is "Likely Not Authentic", then this choice would be entered into CASIE or, if necessary, we could use Table 7, which would yield the numerical IOCs as IOC(1) = 91.7%, IOC(2) = 100%, IOC(3) = 50%, IOC(4)(ROW) = 77.1%. Now the previous "new" POAs are taken as "old" in the formula, that is, S1(old) = S2(old) = S3(old) = 31%, S4(old) = 7%. The updated POAs may then be computed, and an application of the formula (or the computer program) will yield: S2(new) = Segment 2 = 38.6%, S3(new) = Segment 3 = 19.3%, S4(new) = Segment 4(ROW) = 6.7%.
In Section IV, we have presented a method for evaluating clues. The subjective evaluation is accomplished with a two-stage process.
We sincerely appreciate the opportunity to present our thoughts and ideas on search management and the CASIE search software. We feel we have a responsibility to quantify those aspects of search theory and management that can be quantified, but we also realize that some aspects of search and rescue will inevitably remain an art. We must always remember that what the computer or search software suggests should be consistent with our own experience and wisdom. We must avoid the "Garbage In, Garbage Out" trap, which could cost the missing subject's life. It's not enough to be computer literate when using any search software; we also must understand search theory and the principles of search management. We understand that much of the material in these sections (especially the last one) contains complex ideas and computations, not easily digested in the first reading. Our hope is that anyone in the business of conducting searches will refer to them from time to time. We trust that some ideas we have presented here will spark discussions that may help propel search theory and search management a little further into the future. Search theory is a science that we must artfully apply.
 Section II Section III
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