1. Forensic inference – is the law a ass?
BA Festival of Science
6 September 2005
Forensic inference – is the law a ass?
Ian Evett
Forensic Science Service UK
 The Forensic Science Service 2004

2. “If the law supposes that,” said Mr. Bumble...
“the law is a ass – a idiot.”
Charles Dickens: Oliver Twist ch 51.

3. The offender left a small quantity of cellular material...
A crime has been
committed
The offender left a small
quantity of cellular material...
...which has been
DNA profiled
Crime sample
The two profiles
match
...and he has been
DNA profiled also
Suspect sample
A suspect has been arrested...

4. There are two key questions
Crime sample
Match
Suspect sample
What does this mean?
There are two key questions
Did the suspect leave the
crime sample?

5. If I take two samples from the same person – do I expect them
Crime sample
Suspect sample
Match
Key question 1.
If I take two samples from the same person – do I expect them
to give the same DNA profile?
It is almost certain that two samples from the same person would give the same DNA profile

6. *Because we inherit our DNA from our parents,
Crime sample
Suspect sample
Match
Key question 2.
If I take samples from two different persons – do I expect them to have the same DNA profile?
It is very unlikely that two unrelated* people would have the same DNA profile
*Because we inherit our DNA from our parents,
close relatives are much more likely to
share features in their profiles

7. Match What does this mean?
Crime sample
Suspect sample
Match
What does this mean?
If the suspect had left the crime sample, it is almost certain we would see a match
If some other unknown person had left the crime sample, there is a very small chance that we would see a match

8. Did the defendant leave the crime sample?
Suspect sample
Match
Did the defendant leave the crime sample?
The probability of
a match if some other
person had left
the crime sample
is very small
The probability of
a match if the
defendant had left
the crime sample
is very large
Close to one
e.g About one
in a million

9. the Prosecutor’s Fallacy
Crime sample
Suspect sample
Match
A common mistake:
the Prosecutor’s Fallacy
The probability of a match
if the crime sample had come from
someone else is 1 in a million
I see. There is a 1 in a million
probability that the crime sample had
come from someone else...
Hence it is almost certain that the
crime sample came from the defendant

10. The probability of a match if the crime sample had come from
someone else is 1 in a million
I see. There is a 1 in a million
probability that the crime sample did
come from someone else...
The judge has made a serious
mistake. This is known as
the Prosecutor’s fallacy

11. If an animal is an elephant then there is a very high probability
that it has four legs.
Shorthand:
Pr(Four legs | Elephant) =

12. four legs then there is a very high
SO!! - if an animal has
four legs then there is a very high
probability that it is an elephant.
Pr(Four legs | Elephant) =
Pr(Elephant | Four legs) =
???

13. I am interested in the probability that
Crime sample
Suspect sample
Match
I am interested in the probability that
the crime stain was left by the defendant
That depends not only
on the scientific evidence, but also on
other non-scientific evidence
..such as where the defendant was
when the crime occurred

14. Match The court will hear non-scientific evidence. Such as:
time, place, opportunity
what the defendant says
what the witnesses say
It is in the light of that
evidence that they must
consider the evidence of
the matching DNA
Crime sample
Suspect sample
Match

15. In many aspects of our lives we update our uncertainty about
something in the light of
new information

16. I think there is a very good chance that the market in pickled horse chestnuts will
go through the roof
I think there is a good chance that the market in pickled horse chestnuts will collapse
New research has shown that pickled horse chestnuts are a guaranteed cure for baldness

17. Prior
New information
Posterior

18. Non scientific evidence: time, place, opportunity
what the defendant says
what the witnesses say
Prior
belief
DNA evidence
Crime sample
Suspect sample
Match
Posterior belief

19. in the light of new information
Updating uncertainty
in the light of new information
Bayes’ Theorem
Likelihood
ratio
Posterior
Odds
Posterior
belief
New information
Prior
Odds
Prior
belief
= X

20. Did the defendant leave the crime stain? Or did someone else leave it?
Crime sample
Suspect sample
Match
Did the defendant leave
the crime stain?
Or did someone else leave it?
Prior
odds
If the defendant had left the crime stain the probability of a match is approximately one
If someone else had left
the crime stain, the probability of a match is 1 in a million
The match is a million times more probable if the defendant left the crime stain than if someone else left it
Posterior belief

21. DNA match between profile from vaginal swab and Mr Adams
R v. Dennis John Adams
Rape: Hemel Hempstead
DNA match between profile
from vaginal swab and Mr Adams
Match probability
1 in 200 million
Victim said that Mr Adams
did not look like the rapist
Mr Adams had an alibi

22. The central problem in this case was that of combining statistically
R v. Dennis John Adams
The central problem in this case
was that of combining statistically
based scientific evidence in support
of the prosecution...
...with non scientific evidence in
support of the defence

23. To cut a long story short...
R v. Dennis John Adams
To cut a long story short...
...defence argued that the problem should
be approached by inviting the jury to
quantify their assessment of the non-
scientific evidence
...then combining all of the various elements
by means of Bayes’ theorem
There were two trials and two
appeals.

24. ... we have very grave doubts as to whether
R v. Dennis John Adams
... we have very grave doubts as to whether
the evidence relating to Bayes’ Theorem
was properly admissible,
Judgment:
First appeal
...because it trespasses on an area peculiarly and
exclusively within the province of the jury, namely
the way in which they evaluate the relationship
between one piece of evidence and another.

25. ...the attempt to determine guilt or innocence
R v. Dennis John Adams
Judgment:
First appeal
...the attempt to determine guilt or innocence
on the basis of a mathematical formula,
applied to each separate piece of evidence,
is simply inappropriate to the jury’s task.
Jurors evaluate evidence... by the joint
application of their individual common
sense and knowledge of the world...

26. ...the jury ...would have to ask themselves
R v. Dennis John Adams
Judgment:
Second appeal
...the jury ...would have to ask themselves
whether they were satisfied that only
X white European men in the UK would
have a DNA profile matching that of the
rapist who left the crime stain
It would be a matter for the jury, having
heard the evidence, to give a value of X.

27. The probability of finding that profile
Dennis Adams judgment
Crime sample
Suspect sample
Match
The probability of finding that profile
if the crime stain had come from
someone else is 1 in 200 million
How many adult
white males in
the UK would have
that profile?
Approximately one tenth of a man

28. straightforward, isn’t it?
R v. Dennis John Adams
It would be a matter for the jury, having
heard the evidence, to give a value of X.
Well, that’s pretty
straightforward, isn’t it?
X is approximately
one tenth of a man
They would then have to ask themselves
whether they were satisfied that the
defendant was one of those men.

29. ...consideration of the case along the lines
R v. Dennis John Adams
...consideration of the case along the lines
indicated would, in our judgment, reflect
a normal course for a properly instructed
jury to adopt....
It is the sort of task which juries
perform every day.
This appears to be a deliberate
instruction for juries to reason
irrationally

30. Doheny and Adams judgment
Crime sample
Suspect sample
Match
When the scientist gives evidence
it is important that he should not
overstep the line which separates
his province from that of the jury
He will properly explain to the Jury the nature of the match...
He will...give the Jury the random occurrence ratio – the frequency with which the matching DNA characteristics are likely to be found in the population at large

31. Doheny and Adams judgment
Crime sample
Suspect sample
Match
Doheny and Adams judgment
The scientist should not be asked his opinion on the likelihood that
it was the Defendant who left the crime stain,
...nor when giving evidence should he use terminology which may lead the jury to believe that he is expressing such an opinion

32. Either: the defendant left the crime stain
Crime sample
Suspect sample
Match
Either: the defendant left the crime stain
Or: some unknown person left the crime stain
The evidence is a million times more probable if the first proposition is true
This is extremely strong support for the first proposition
That statement is counter to the Doheny/Adams judgment.

33. Either: the defendant wrote the questioned handwriting
Or: some unknown person
wrote it.
In my opinion, there is extremely strong support for the first proposition
Thank you, Dr Bloggs, that is very helpful.

34. Thank you, Mr Holmes - that is
In my opinion, the crime mark and control print were made by the same person.
Thank you, Mr Holmes - that is
amazingly helpful.

35. If an expert is unable to carry out a statistical
The present position
If an expert is unable to carry out a statistical
assessment of the weight of the evidence*
then courts allow him to express an opinion
of identity of source
If an expert is able to carry out a statistical
assessment of the weight of the evidence** then
courts will not allow him to express an opinion of
identity of source - the statistic is put to the jury
* e.g. fingerprints, handwriting, toolmarks, footwear
** DNA profiling

36. It is our hope, as forensic scientists,
that expert opinions will increasingly
be based on databases and sound
statistical methods
The DNA experience suggests that if
the weight of evidence can be measured
by a numerical statistic....
...then it is the statistic that should be
put to the jury, rather than an expert
opinion of identity of source

37. ...then it is the statistic that should be
put to the jury, rather than an expert
opinion of identity of source
Most forensic scientists have no
problem with this view...
Nevertheless, it would seem desirable
that we should explore with the judiciary
and the legal profession ways
of presenting statistical evidence...
...in a manner that is
balanced, robust
and logical

38. The most rational compromise would be to explain the meaning of the
likelihood ratio
And present illustrations based on
a range of priors agreed by the court

39. The probability that the defendant
Crime sample
Suspect sample
Match
The evidence is a million times more probable if the defendant left the crime stain than if some unknown person left it.
The probability that the defendant
left the crime stain depends on this evidence and also all of the other evidence

40. Crime sample
Suspect sample
Match
I can illustrate the weight of evidence associated with the DNA match by some illustrative examples

41. ? Non-scientific evidence
If a person thought, based on the non-scientific evidence that the probability that the defendant left the crime sample is very small....say a one in a thousand
Crime sample
Suspect sample
Match
A match is a million
times more probable if
he left it than if some
unknown person left it
...the effect of the DNA evidence is to turn that into a 99.9% probability that the defendant left the crime sample

42. Several illustrations could be presented,
according to the requirements of the court
This would set the DNA evidence into the context of all the other evidence in a balanced, robust and logical manner.

43. So – is the law a ass?

44. Don’t ask me
folks!