July 31, 2013

“10 quadrillion times more likely to have done it”

Thomas Lumley, tipped off by Luis Apiolaza on Twitter, pointed me to this article in the NZ Herald.

The article is yet another example of the Herald’s inability to correctly report DNA statistics. It makes the following statement:
This article reports a quote from the Crown Prosecutor, paraphrased as follows:

A man charged with raping a woman during a kidnap has pleaded not guilty but Crown says DNA evidence shows the man was “10,000,000,000,000,000 times likely” to be responsible for the crime.

To be fair to the article’s author, this may have been the statement that the Crown prosecutor made, but nNo forensic scientist in New Zealand would say this. ESR scientists are trained to give statements of the following type:

“The evidence is 1016 (=10,000,000,000,000,000) times more likely if the defendant and the victim were contributors to the stain, rather than the victim and someone unrelated to the defendant.”

It is extremely important to note that This is a statement about the likelihood of the evidence given the hypotheses rather than the other way around. A forensic scientist is bought to court to comment on the strength of the evidence and specifically not on whether the defendant is guilty.

I have commented on this before., and sent correspondence to the NZ Herald numerous times. Perhaps a mention on StatsChat will inspire change.

Update: The NZ Herald reporter, James Ihaka, has contacted me and said “The statement came from a Crown prosecutor about the evidence that the forensic scientist will present later in the trial. Taking in to consideration what you have said however, it would probably be more accurate to rephrase this.” Good on you James!

Update 2: James Ihaka has contacted me again, with the following information:

This is the direct quote from Crown prosecutor Rebecca Mann: ( I checked with her)
“It is ten thousand million million times more likely for the DNA these samples originated from (the complainant) and Mr Martin rather than from (the complainant) and another unrelated individual selected at random from the general New Zealand population.”

I apologize unreservedly for attributing this to James Ihaka, and again congratulate him for following it up.

The statement Ms. Mann should have given is


The evidence (the DNA match) is ten thousand million million times more likely if these samples originated from (the complainant) and Mr Martin rather than if they originated from (the complainant) and another unrelated individual selected at random from the general New Zealand population.”

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James Curran's interests are in statistical problems in forensic science. He consults with forensic agencies in New Zealand, Australia and the United Kingdom, and produces and maintains expert systems software for the interpretation of evidence. He has experience as an expert witness in DNA and glass evidence, appearing in courts in the United States and Australia. He also very strong interests in statistical computing, and in automation projects. He is also a director of the University of Auckland's Bioinformatics Institute. See all posts by James Curran »

Comments

  • avatar

    ““The evidence is 1016 (=10,000,000,000,000,000) times more likely if the defendant and the victim were contributors to the stain, rather than the victim and someone unrelated to the defendant.””

    Does this mean that Prob(data | a relative did it) is also pretty high? What’s the likelihood ratio for that?

    9 months ago Reply

    • avatar
      James Curran

      It would be substantially smaller than 10^16 Brendon, but it would still be a fairly large number. However, without the case data I couldn’t you specifically.

      Your question also raises an interesting point – “which relative” or “any relative.” The question is easy to answer for a specified relative such as a brother or cousin, but less so for a non-specific relationship. To answer this we’d need to consider multiple alternative hypotheses, which Bayes’ Theorem allows, but we would also need sensible values for Pr(Brother), Pr(Cousin) etc.

      9 months ago Reply

  • avatar
    Clarissa Kramer

    What would it be if it was 8.2 million times more likely is that a positive result or is it just another scare tactic they use. Please help thanks

    4 months ago Reply

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