Tuesday 15 January 2013

Who is the appropriate expert here: a DNA specialist or a probability specialist?

An interesting issue about expert evidence has arisen in a case on which I am providing input. It can be summarized as follows:

If a DNA expert makes an incorrect probabilistic inference (such as a logical or computational error) arising from a DNA probability, is it appropriate for a probability expert to point out the error or is only a DNA expert qualified to point out the error?

According to many lawyers only a DNA expert is qualified. I believe this is fundamentally wrong, as the following real (but anonymized) example demonstrates:

A partial DNA sample found at the scene of the crime (containing only two clearly identifiable components)  matches the defendant's DNA.  The DNA expert (who we will refer to as expert A) concludes:
"the probability this DNA comes from anybody other than the defendant is very unlikely". 
A probability expert (expert B) believes that the DNA expert's conclusion may be highly misleading; Expert B asks an independent DNA expert (expert C) to check the DNA evidence and provide a match probability. Expert C confirms a two-component match and asserts that the match probability is about 1 in a 100, i..e. the probability of finding such a match in a person not involved is 1 in 100. Expert B uses this information to explain why expert A's statement was misleading as follows:
Expert A is making a statement about the probability of the defendant not being the source of the DNA, when all that expert A can actually conclude is that the probability of getting such a DNA match if the defendant is not the source is 1 in 100. If the term 'very unlikely' is a surrogate for the more precise "1 in 100 probability" then the expert is making the transposed conditional error (prosecutors fallacy). Specifically one cannot make any conclusions about the (posterior) probability of the defendant being or not being the source without knowing something about the prior probability - i.e. without knowing how many other people could have left the DNA sample at the scene. If, for example, there are 1000 people who have not been ruled out then about 10 of these would have the matching partial DNA. In that case "the probability this DNA comes from anybody other than the defendant is about 90%" - which is very different from expert A's conclusion. 
A lawyer rejects expert B's contribution because it is "outside his area of expertise", stating the following:
Expert B is not an expert on DNA - as is proved by the fact that he had to ask another DNA expert (C) to come up with the relevant random match probability - and so is not qualified to comment on DNA evidence.Only a DNA expert can comment on the likelihood that the DNA comes from the defendant.

But expert B is NOT commenting on the DNA evidence. Expert B is commenting on a logically incorrect - and unnecessarily vague - probabilistic inference made by a person who happens to be a DNA expert. In fact the only person here who is venturing outside their area of expertise is expert A because he/she has made an assumption about something which he/she has no information or expertise - namely the number of people who could potentially have been at the scene of the crime.

The logical extension of the lawyer's argument would be to reject all logical, mathematical and statistical analysis about a problem X if it is not presented by a person who is an expert in problem X.