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Making the Court Understand
and Use the LR
From Gut Feeling to Rational Evaluation of Odds
Copenhagen, April 2015
Jakob Larsen, ph.d
[email protected]
Making the Court understand and use the LR
Slide 1
ISFG Recommendation
Even if the legal system does not implicitly appear
to support the use of the likelihood ratio, it is
recommended that the scientist is trained in the
methodology and routinely uses it in case notes,
advising the court in the preferred method before
reporting the evidence in line with the court
requirements. The scientific community has a
responsibility to support improvement of standards
of scientific reasoning in the court-room.
Slide 2
Overview
To speak ”legal” and ”forensic” – two different languages
Education of users of forensic DNA investigations
What the users of the LR should know
Courses
Cooperation with lawyers/prosecutors/judges
Multidisciplinary publications
e-learning/FAQs
Communication of DNA evidence in Denmark
Mathematical basis for understanding DNA evidence
LR or verbalised translation?
Illustration of random match probability
Illustration of LR
The court's use of Bayes theorem
The major fallacies
Does it work?
Slide 3
The court and the scientist do not speak the same
language
Slide 4
For a person with a scientific background
NOTHING is completely sure
Are you sure that
the sun will rise
tomorrow…?
Slide 5
No … not
completely.
But it is a very
good theory!
Lawyers are comfortable with words, scientists are
happy with numbers
Is it proved
Maybe… almost.
beyond reasonable
The probability is
doubt…?
That was not
0,99!
much…? It’s usually
1.000.000, isn’t
it…?
Slide 6
Education of users of forensic DNA investigations
in Denmark
National Danish Police 3 days Crime scene investigators
The Public Procecutor
1 day
Procecutors, judges, defense attorneys
The Public Procecutor
½ day New Procecutors
Court Administration
1 day
The Judge Acadamy
½ day Judges
Judges
National Police School 1 hour Experienced investigators
The attorneys Society/ Varies Defense attorneys
Danish attorneys
Slide 7
The court should…
Be able to communicate evidential weight correctly
Be able to use Bayes theorem
Recognize and avoid prosecutors fallacy
Recognize and avoid defense attorneys fallacy
Be aware of risks
Contaminations
Mix-ups
Close relatives
Other errors
Be able to distinguish between cases where the defendant is found due to a
DNA database hit, and where the defendant was suspected before the
DNA evidence was known
Slide 8
Typical reactions from the law people
• ”Is this something you have made up at the christmas party”?
• ”We are going to decide whether the defendant should behind bars for many
years. We need proof – not probabilities”
• ”Isn’t the DNA evidence 100% proof? Then it is only circumstantial evidence –
in contrast to the fingerprint”
• ”Actually, I have always evaluated evidence this way – I have just used Bayes
theorem with my gut feeling”
• This is just what I have been missing! It can – in principle - be used to assess
all kind of evidence in a rational way. Why do we not learn this in college?
Slide 9
Before the course: Exercises
How can DNA evidence typically be used in connection with a
crime case?
What aspects of DNA evidence do you find most difficult to use
and communicate in court - and why?
What specific benefits do you expect from the course on DNA
evidence?
Slide 10
The purposes of the pre-course exercise are
multiple
Forces the student to think about forensic genetics in
advance – increases the yield
Forces the student to realize the expected benefits of
the course
Tells the teacher(s) what aspects of forensic genetics,
that are the most difficult to understand
Slide 11
Cooperation with a specially trained lawyer
Who?
Independent lawyer who has special
knowledge about DNA evidence, and can
translate from “forensic" to “juridical".
University
Judge
How?
Contributions to readily-available presentations
Contributions to teaching
Monitoring of legal trends
Judge Kari Sørensen,
Court of Frederiksberg
Slide 12
Multidisciplinary publications: Bayes theorem, prosecutors
and defense attorneys fallacy
Slide 13
Multidisciplinary publications: DNA profiles from one or more
persons, frequency databases, transfer of DNA, uncertainty,
etc.
Slide 14
E-learning
https://intranet.ku.dk/Sider/default.aspx
Slide 15
If you choose to report the likelihood-ratio
Numbers are unambiguous
Easy to use in Bayes theorem
Slide 16
Difficult for the court to
understand
Readily leads to the fallacies
"We should not use
probabilities, we need proof”
If you choose to report verbalized translations of
the LR
The court is accustomed to
verbal declarations of weights
Easy to communicate in court
Slide 17
Different people perceive words
differently
Necessary to use intervals
Difficulty in applying Bayes theorem
Mathematical basis for understanding DNA
evidence
Probability
Conditional probability
P (6 even)
Independent events
Odds
P( E )
Odds( E ) 
1  P( E )
Slide 18
What does the LR mean to the court?
How the court may apply the LR “mathematically
correct”
Likelihood of DNA profile if stain originates from defendant
Likelihood of DNA profile if stain originates from random alternative
LR =
PROBLEM IN COURT
ODDS =
Probability that stain originates from defendant given info and DNA
Probability that stain does not originate from defendant given info and DNA
”If LR is 1.000, odds will increase by a factor of 1.000,
when the DNA-evidence is taken into account
Bayes theorem:
Slide 19
POSTERIOR ODDS = LR x PRIOR ODDS
Odds for guilt, ”odds for innocence” and doubt
Odds for guilt =
Probability that stain originates from defendant given info and DNA
Probability that stain does not originate from defendant given info and DNA
Odds for innocence = Probability that stain does not originate from defendant given info and DNA
Probability that stain originates from defendant given info and DNA
Odds for innocence = doubt
”If LR is 1.000, doubt is reduced 1.000 times, when the
DNA evidence is taken into account”
Bayes theorem:
Slide 20
POSTERIOR ODDS = LR x PRIOR ODDS
Sit down, and stay seated if you are not...
Match probability
Wearing a belt
Having blue eyes
Went skiing last year
The owner of af black car
The parent of three or more children
Having coins in your pocket
Born in January
Had oat meal this morning
The owner of three or more fishing rods
Wearing glasses
0,80
0,30
0,08
0,20
0,10
0,20
0,08
0,20
0,12
0,30
Combined match probability
1:12.000.000
Slide 21
Relate the size of the match probability to
probabilities the court is familiar with
P(Unlock a 3-digit pad lock)
P(guess a PIN-code)
P(make ”yatzy” in one roll)
Slide 22
Relate the LR to evidential weights the court is
used to evaluate
The weight of a testimony (assume the witness is wrong one out of
25 cases)
The weight of the last two digits of a license plate from a
perpetrator car matching that of the defendant
The weight of a fingerprint match
The weight of the defendants statement: “Not guilty"
Slide 23
It’s 1000
times less
than
1.000.000
Slide 24
It’s 1000
A likelihood ratio that is times
What
1000
do you
– is this
think??
a lot? more than
1
Procecutors fallacy
The DNA profile of the stain, is one million times more
likely if the stain actually comes from the defendant
than if the stain comes from a random other person in
the relevant population.
LR =
Likelihood of DNA profile if stain originates from defendant
Likelihood of DNA profile if stain originates from random alternative
It is one million times more likely that the stain comes
from the defendant than the stain comes from a
random other person in the relevant population.
ODDS =
Probability that stain originates from defendant given info and DNA
Probability that stain does not originate from defendant given info and DNA
Slide 25
The horse analogy
P ( 4legs horse)
P ( horse 4legs )
Slide 26
Aha, if LR is 1,000,000, it must mean that the probability
that a random person matches is 1:1,000,000.
So there must be some five persons in Denmark,
the stain is just as likely to originate from ...?
Slide 27
Defense
attorney’s
fallacy!
Defense attorney fallacy
If the likelihood-ratio is 1,000,000, then the match probability is 1
in 1,000,000. In a population as the Danish, (approximately
5,000,000 inhabitants) there will most likely be five individuals
matching the DNA profile.
However, this does not mean that these five individuals are equally
likely originators of the stain, because this would imply that the
prior odds should be the same for all citizens in Denmark.
The vast majority of the Danish population will for practical
purposes be excluded as the originator of the stain, ie the prior
odds are very low or zero.
DAF is committed, if you put the weight of the DNA evidence in
relation to the size of a population and thus assume that all
members of the population have the same prior-odds.
Slide 28
Exercise / repetition
Identify “prosecutors fallacy" and "defense attorneys
fallacy" in the following (not hard to find examples!)
Published sentences
Crime sections of newspapers
Legal literature
Try to consider the weight of other evidence with a
likelihood-ratio, use Bayes theorem and see if it makes
sense.
Slide 29
Does it work?
”Prior odds”, ”Likelihood ratios” and combined
probabilities are increasingly discussed in Danish
courts.
The testimony frequency is decreasing
How much more in addition to the ”more-than-a-millionLR” do we need if we want to be ”beyond reasonable
doubt”?
Cases, where the prosecutor has estimated the LR of
non-DNA evidence
Slide 30
Thank you for your attention!
Questions?
[email protected]
Slide 31