The measures of likelihood discussed above are population level estimates of the accuracy of the method and refer to the strength of matches between images that are known to have repeats in a test population. These results beg two questions regarding the application of this method in the forensic setting. First, how will this method be applicable in the forensic setting and second, what is the probability of an individual match using this method?
The answer to the first question is that the method can be applied in the identification of a set of forensic remains by incorporating the measurement data collected from the image of the deceased into the present data set, and using the nearest neighbor algorithm to generate a match from within that population. The answer to the second question is the most important measure of the
accuracy of matches made with this method, and is discussed in detail in the following paragraphs.
Probability of a correct match
In answer to the second question, the actual Euclidean distance between matched images was used to evaluate to the strength of the relationship
between them, and the probability that they represent the same individual. The smaller the distance, the more likely it is that the association between them represents a correct match. Thus it was important to generate an estimate of the probability of a correct match for the various Euclidean distances that separate the matches in this data set. This involved establishing: (1) the
approximate Euclidean distance greater than which matches lost sufficient probability of correctness to be considered accurate, and (2) the approximate Euclidean distance below which the probability of a match is high enough to consider the match to be accurate.
There were no incorrect matches made using the biological model when the Euclidean distance between the nearest neighbors was 32 or less, and no incorrect matches were made using the PCFA model when the distance
between repeats was 37 or less. This is because there was no smaller distance between any of the comparisons than between the repeat images. This means that the probability that a match between nearest neighbors would represent a correct match is 100% when the Euclidean distance between them is less than 32 or 37 for the biological and PCFA models, respectively.
However, this does not mean that either 32 or 37 represent thresholds past which all matches are suspect. Instead, these numbers represent indicators of the range of distances beyond which incorrect matches become increasingly common. For instance, the Euclidean distance between images was 33 for eight comparisons. Of those, three were comparisons between repeat images, and the other five were between non-repeats. This means that if the Euclidean distance between ante- and postmortem images used in a
forensic case is 33, there is only a 37% chance that the two images represent the repeat images from the same individual. Figure 8.1 displays this relationship graphically.
Figure 8.1. Scatterplot of distances between compared images and the probability that those comparisons represent a correct match with fitted regression line for the Biological Model.
The regression line in Figure 7.1 suggests that the probability of a correct match diminishes dramatically when the Euclidean distance between images approaches 30. Thus, in the forensic setting, a nearest neighbor match of images that are separated by less than 30 Euclidean distance units can be considered very reliable, and this reliability diminishes dramatically with larger distances. Nearest neighbor matches between images that are 40 or more Euclidean distance units apart rarely represent a correct match.
In theory this is because there should technically be no separation in Euclidean space between two images taken from the same individual if all error is eliminated. However, since error in measurement is unavoidable, the small
distances that separate repeat images in this sample are probably the result of summed measurement error, and generally don’t result in a total distance of more than 30. On the other hand, real biological variation in landmark location is less systematic and often more significant than measurement error, and
generally results in a distance between images that is greater than 45. Those individuals whose images are separated by Euclidean distances between these two values are marked by a less systematic pattern of measurement error, but not by biological variation in their dimensions. The greater differences between the images of these individuals appears to be the result of combined error of measurement in landmark placement and slight variation in the axial plane between the images being compared. Repeat measurement of a sample of both of the images of ten of these individuals yielded variation that was within the range of variation of standard measurement error, and did not result in change sufficient to move the images significantly, either closer in Euclidean distance or farther apart. This suggests that the repeat measures recaptured variation due to variation in the axial plane, and supports the notion that variation in the axial plane is what resulted in the placement of these individuals within the range of overlap between matches and non-matches.
Similar accuracy characterizes both the biological and PCFA models. Both achieve more than 95% correct classification, and very high likelihood ratios. It is thus difficult to favor one over the other for use in the forensic setting. The PCFA model incorporates 39 measurements between 26
landmarks, and the biological model incorporates 30 measurements between 23 landmarks. Whereas the number of measurements incorporated does not complicate the use of a model because the measurents are calculated from the landmarks and not directly measured, the increased number of landmarks incorporated in the PCFA model may make it more difficult to apply in forensic investigations as well as more prone to error in data collection. The three landmarks that are incorporated into the PCFA model but not in the biological model are the center point of the middle ear (MID), the lateral limit of the jugular canal (JUG), and the vestibule (VBLE). Of these, JUG and MID are both difficult to locate relative to the other landmarks because of their less definitive location. For example, the large diameter of the middle ear may result in more variable estimation of its center (MID) in relation to features with smaller diameters like the semi-circular canals. Locating JUG requires placement of a control point on the boundary of a foramen that also has a large diameter. The open nature of the resultant curve of the boundary along which the point is placed may also result in greater error than the smaller landmarks incorporated in the biological model. The vestibule should not introduce any further error into the model because it is easily located and there is little variation in the location of its center point.
Nevertheless, because the PCFA model requires the collection of more landmark data (3 more landmarks than the biological model), and because of the more diffuse nature of two of the additional landmarks (MID and JUG), I suggest