Biology Reference
In-Depth Information
Table 9.1
Verbal scales for likelihood ratios
Likelihood ratios
Verbal equivalent
1-10
Limited support for prosecution hypothesis
10-100
Moderate support for prosecution hypothesis
100-1000
Moderately strong support for prosecution hypothesis
1000-10 000
Strong support for the prosecution hypothesis
>
10 000
Very strong support for prosecution hypothesis
Further, there is no rationale for the boundaries, for example to discriminate between
a likelihood ratio of 99 and one of 101.
The Bayesian approach
The Bayesian approach is favoured by many forensic scientists but has not gained
widespread usage in the presentation of DNA evidence. The approach builds upon
the likelihood but allows non-scientific data to be introduced in the form of prior
odds. The non-scientific data will update the likelihood ratio to produce the final
odds either in favour of or against the proposition put forward by the prosecution or
defence (Equation 9.4).
Pr
H
p
Pr
H
d
x
Pr
(
E
|
H
p
)
Pr
(
H
p
|
E
)
H
d
)
=
Pr
(
E
|
Pr
(
H
d
|
E
)
(
or prior odds
×
likelihood ratio
=
posterior odds
)
(9.4)
Consider the case against Dennis Adams (
R
v
Adams
[1996] Cr. App. R., Part 3)
in the UK where he was accused of a rape that occurred in 1991. The trial was in
1994 when the DNA profiling methodology was based upon VNTR analysis that
pre-dated STR typing. The DNA evidence put forward by the prosecution was that
the DNA profile occurred in 1 in 200 million of the population. Adams pleaded not
guilty; he had an alibi and was not identified at an identity parade. The defence
expert produced numerical values for the crime being committed by a local man,
for the possibility of not being identified at the parade and for the alibi. All these
prior probabilities were multiplied to determine the prior probability. The defence
argued that the evidence (genetic and non-genetic) indicated the innocence of the
accused. At the trial the judge allowed this to happen and directed the jury that they
could use the Bayesian figure if they wished. Adams was found guilty.
The use of Bayesian evaluation of DNA evidence in the UK legal system has not
been accepted and has led to successful appeals against convictions, including the
above example, when the Appeal Court took the view that the use of Bayesian statis-
tics trespassed on areas exclusively and peculiarly those of the jury. The relationship
between different pieces of evidence was for the jury to decide and the mathemat-
ical formula might be applied differently by a different set of jurors. Jurors should
evaluate the evidence by the joint application of their common sense and knowledge
