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On the Role of Statistics in Miscarriages of Justice
Norman Fenton
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Invited statement at the third meeting of the All-Party Parliamentary Group on
Miscarriages of Justice, hosted by APPG chair Barry Sheerman MP
25 June 2018, House of Commons
1. I would like to thank Jon Robins for inviting me to this event and congratulate him on his
outstanding book
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.
2. My work focuses on probabilistic risk assessment in critical decision making. I have a
special interest in improving probabilistic and statistical reasoning in the presentation and
analysis of legal (notably forensic) evidence, and I lead an international consortium of
mathematicians, forensic scientists, and lawyers with this objective
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. I have acted as an
expert witness or consultant in many major civil and criminal cases where probability and
statistics have been an issue.
3. I believe that probability and statistics could and should be used more widely in
analysing legal evidence. A lot of the work I have been involved with has shown that
explicit use of probability and statistics can reveal fundamental errors of reasoning that
were hidden or implied by either forensic experts or lawyers. However, while probability
and statistics can and should be used as a force for good, where statistics have been
explicitly used in court, more often than not their presentation, reasoning and
interpretation has been fundamentally flawed and this has contributed to miscarriages of
justices.
4. For example, basic probability reasoning would have revealed the flaws in the
presentation of the Griess test evidence in the Birmingham six case; in this example the
fact that handling explosives is very likely to produce a positive test result was wrongly
interpreted as meaning that the observed positive test result meant handling explosives
was very likely. This is a well-known error called, for very good reason, the prosecutor’s
fallacy. In the case of Eddie Gilfoyle, the extremely low probability quoted for a pregnant
woman to commit suicide (1 in a million) may have been wrongly confused with the
probability of Eddie being innocent of murder. The fallacy occurs frequently with any type
of forensic match evidence including DNA. I have seen many examples where the true
probative value of DNA match evidence has been massively overestimated - with judges
and juries being swayed by such evidence to return a guilty verdict when all other
evidence supports innocence.
5. The same is true when there are multiple pieces of coincidental evidence against a
defendant, which are collectively claimed to be so great that they ‘prove’ guilt –
prosecutors say “there is no such thing as coincidence” in such cases. The case of Sally
Clark is especially tragic. Clark was convicted for the murder of her two young children
who had died one year apart. To counter the hypothesis that the children had died as a
result of Sudden Infant Death Syndrome (SIDS) rather than murder the prosecution’s
expert witness stated that there was “only a 1 in 73 million chance of both children being
SIDS victims”. This figure was not only wrong, being based on a basic probability error
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Professor of Risk and Information Management, Queen Mary University of London and Director of
Agena Ltd. (n.fenton@qmul.ac.uk)
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Robins, J. (2018). Guilty Until Proven Innocent: The Crisis in Our Justice System. Biteback
Publishing.
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https://www.researchgate.net/project/Bayes-and-the-Law
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that assumed two SIDS deaths in the same family were independent, but was also
presented in a way that may have led the jury into the prosecutor’s fallacy.
6. At the extreme, coincidental evidence may lead to what we would call a statistics-led
prosecution case which is fitted around the fact that one person is connected to a
number of related events. The Lucia de Berk case in Holland is a classic example of this.
In this case nine unusual deaths occurred at the same hospital. Although none of the
deaths were initially considered suspicious, it was claimed that one nurse – Lucia de
Berk – was on duty during each of these deaths. The probability of such a sequence
happening by chance was wrongly stated in court as being 1 in 342 million. Once it’s
decided that this cannot be coincidental ‘confirmation bias’ generally leads to finding
multiple pieces of circumstantial evidence against the defendant. In this case ambiguous
diary entries about a ‘great secret’ and a passion for tarot card readings were treated as
evidence of murderous intent. Medical evidence supporting natural deaths was ignored
while erroneous evidence supporting poisoning in 2 of the deaths - was found. Lucia de
Berk was convicted of 7 murders in 2004 but was ultimately found not guilty on appeal in
2010.
7. There are clear similarities with the case of Ben Geen who was also a nurse convicted of
two murders and several attempted murders. The Dutch statistician Richard Gill who had
been instrumental in exposing the statistical flaws in the Lucia de Berk case alerted me
to the Ben Geen case and asked me to conduct my own statistical analysis. I did this
voluntarily and was one of the probability experts who submitted reports to the CCRC.
Focusing only on the statistics – and not the medical facts of the case – my interest was
in whether a cluster of events (respiratory arrests) happening within a short period of
time at one hospital where the same nurse was present is genuinely unusual.
8. My initial feelings were that, as in many similar examples I have seen, the ‘extremely
unlikely coincidence’ was not as unlikely as most people initially assume. ‘Coincidences’
which appear almost impossible often actually have a very high probability of occurring.
If you observe a person rolling a 6-sided die 5 times and getting a six each time you
would think he was cheating – the probability of that happening by chance is 1 in nearly
8000. But, if there are 20,000 people rolling a die 5 times then it would be extremely
unlikely that less than 2 of them would roll 5 sixes.
9. Similarly, what I showed in my report to the CCRC was that, using standard statistical
methods and assumptions, it turns out that the extent to which the cluster of events
observed in the Ben Geen case (18 in a 2-month period) is not at all unusual. Given
the number of hospitals in the UK, in any 4-year period it is almost certain that there will
be several instances of exactly this kind of “abnormally high” sequence of respiratory
events. It is actually quite likely that, purely by chance, in at least one such sequence
there will be the same nurse present at each event.
10. Finally, I would like to point out that I believe the behavior of the Criminal Cases Review
Commission with respect to my own evidence has been appalling in this case. They
attempted to discredit my evidence based on a demonstrably flawed accusation. Despite
multiple letters written asking for an explanation and apology I never even received even
an acknowledgment from them.
See also: Fenton N.E, Neil M, Berger D, “Bayes and the Law”, Annual Review of Statistics and Its
Application, Volume 3, 2016 (June), pp 51-77 http://dx.doi.org/10.1146/annurev-statistics-041715-
033428 Open access version:
www.eecs.qmul.ac.uk/~norman/papers/bayes_and_the_law_revised_FINAL.pdf