Prosecutor fallacy again in media reporting of David Burgess DNA case

There are numerous reports today of the trial of David Burgess accused of killing Yolande Waddington in the 1960s. Burgess had been ruled out as a suspect at the time of the crime because his blood was found not to match that of blood on a sweater belonging to Yolande. However, new DNA analysis has found that Burgess's DNA profile does match that of blood found on a sack that was at the crime scene.

Following on from previous blog postings it is clear that again reporters are making the prosecutor fallacy even though it appears not to have been made in court (but as I explain below I believe that other errors were made in court). For example, the Sun provides a classic example of the prosecutor fallacy:

Scientists said the chances of the DNA on the sack not belonging to him were less than “one in a billion”. 

However, both the Mail and Guardian report what I assume were the actual words used by the forensic scientist Mr Price in court:

... the probability of obtaining this result if it is due to DNA from an unknown person who is unrelated to David Burgess is smaller than one in a billion, a thousand million.

Ignoring the fact that all kinds of testing/cross contamination errors have not been factored in to the random match probability of one in a billion, then there is nothing wrong with the above statement because if we let:

• H be the hypothesis "DNA found at scene does not belong to defendant or a relative".
• E be the evidence "DNA found is a match to defendant".

Then the probability of E given H (which is what is stated in the above quote) is indeed one in a billion.

But what is VERY interesting is that Burgess was ruled out in the original investigation because his blood type did NOT match the sample from the scene. To explain the 'change' we get the following quote in the Guardian article:

"Mr Price said the initial test on the bloodstained sweater may have been flawed and that the difference between Burgess’s blood type and that found on the sweater could be due to a mistake in the process that was known to occur sometimes."

In other words the forensic scientist claims that the lack of a positive blood match first time round is "due to a mistake in the process" but he appears never to consider the possibility of any mistake in the process leading to a positive DNA match. Perhaps conveniently for the CPS it appears the sweater has somehow got 'lost'  (curious how that crucial crime scene item should vanish whereas the sack which was never tested orginally should remain) so there was no attempt to test the DNA of the blood on the sweater.

If the latest ruling from the USA is anything to go by, there is going to be even less less chance of questioning the accuracy of DNA and other types of forensic analysis in future.