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part of the prior odds; in any case, prior odds provide a perfect vehicle for
each advocate to proffer the hypothesis that best supports her case. The
Bayesian framework provides a way for integrating the physical evidence
results into the rest of the case.
3.
Classification
We will not attempt a lengthy mathematical treatment of classified evidence.
The breadth and the depth of such a discussion precludes its inclusion here,
and several excellent treatises cover the subject (Robertson and Vignaux,
1995; National Research Council, 1996; Cook et al., 1998a,b; Evett and Weir,
1998). However, one example using likelihood ratios will illustrate the use-
fulness of the method.
The evidence involved is DNA. A woman relates that she and her boyfriend
engaged in consensual sex early in the morning and, as she was seeing him
off to work, she was attacked from behind as she stood on her porch. The
assailant dragged her back into the house and raped her. The victim imme-
diately reported the rape, and was examined at the local hospital. A vaginal
swab was taken, and DNA analysis was performed. Results of the RFLP
analysis showed a mixture of DNA in the sperm fraction. Either three or
four bands were seen at each locus, implying two donors. Reference samples
from the boyfriend and the suspect showed that all of the bands in the
evidence profile could be attributed to a combination of their separate
profiles. Thus, the suspect could not be eliminated as a potential donor to
the sperm fraction. This leads to the inference that the suspect was one of
the semen donors.
The task is now to assess the strength of the inference. Some analysts
insist that a calculation summing all of the possible contributors (sometimes
called random man not excluded, or RMNE) is the most relevant expression.
This calculation does address the concerns of the defendant (perhaps a single
suspect arrested in a case of multiple rapists) who wants to know, “What is
the probability of picking one person at random from the population who
would not be eliminated as a potential donor?” However, the RMNE
approach ignores the fact that two donors are present, and once the types of
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Principles and Practice of Criminalistics
one donor are identified, the types of the other are fixed. Merely summing
the frequency of every potential donor ignores information we have about
the data and fails to represent the complexity of the evidence adequately.
Alternatively we can use an LR to compare competing hypotheses. In our
example, the most relevant and reasonable hypotheses are:
• The mixture was left by the boyfriend (
B
) and the suspect (
S
).
• The mixture was left by the boyfriend (
B
) and an unknown random
unrelated person (
X
).
• The mixture was left by the suspect and an unrelated person (
X
) (i.e.,
not accepting the victim’s story at face value).
• The mixture was left by two unknown random unrelated individuals
(
X
) and (
Y
) (i.e., not accepting the victim’s story at face value).
We first evaluate the probability of each hypotheses separately,* then
compare them using likelihood ratios as follows: