[MUSIC] Welcome to this new video. So on that specific issue of independence between it's worth listening to Professor Darwit on that point. >> Good morning, Professor Phil Darwit. We have just studied in our course some criminal cases. For example, the Collins case, and the Sally Clark case. Where there were problems regarding the assignment of probabilities. You have been involved as a statistician in several criminal cases where there were statistical and inferential issues. Could you please at first present yourself, Professor Darwit? And tell us how you got involved in some of these cases, and particularly in the Sally Clark case? >> Okay, I was for many, many years Professor of Statistics at University College London and through that I got connected with one of the law professors there. A wonderful guy who pointed out to me that there were some fascinating problems in the statistics and the law, which I hadn't been aware of. Through him, I got one or two invitations to get involved in law cases and eventually I was contacted to be an expert witness. At the first appeal of Sally Clark, the trial had taken place without any statistical input whatsoever on either side. Although there was pseudo statistical evidence presented. >> Perfect, thank you very much, thank you very much. If you have time for two more question? >> Yeah. >> First, I would like to ask you, how did you react to the Court of Appeal ruling in the Sally Clark case and how did the lordships deal with the statistical argument? >> Well, just to lay the background, I was one of two statistical experts called in that appeal. Ian Evert from the Forensic Science Service was the other one. We had both prepared long, detailed, and carefully considered reports on the statistics, which were before the three judges of the Court of Appeal. And we were asked to turn up in court so we could give oral evidence on the witness stand. In the event we weren't asked to appear, because when the defense counsel asked us to testify, the lead judge said, well, we don't need to hear from them. This would only be argumentative, and anyway, it isn't rocket science is it? So we never presented our arguments. I dont know if the learned judges even looked at our reports. Judging by the outcome of that, it appears. If they did look at them, they certainly didn't take in the arguments. Briefly, the arguments were two-fold. One, which had a lot of attention in the media and elsewhere, but was actually the least important, was whether we can multiply probabilities assuming independence. And therefore compute a very low value, one at 73 million for the probability that these two babies had died of natural causes. I always try to argue that, whether that number was right or wrong, one couldn't dispute the fact that the number was very, very small. So the logical issue was where there's such a very small probability of the children dying from natural causes was in itself, probative on how to use that value. Can it be used by itself? I argued no, it can't and for example, you have to consider an alternative hypothesis. In this case, the hypothesis that they were murdered by the mother. And on that hypothesis is even more unlikely. I tried to put that argument and I was pretty upset by the way the courts dealt with the fact, essentially they didn't deal with it, they ignored the arguments completely. As I'm sure you know the case eventually went to a second appeal at which the verdict was quashed as unsafe. But that was on medical grounds and not anything to do with the statistics of the case. >> Thank you very much. Thank you very much for this explanation. Let me just finish with our last question for you. As a statistician, what will be your recommendation as to the best way to present statistical evidence in court on forensic science matter? >> Well, I've appeared in a number of cases, always for the defense. And I'm not sure that I can answer your question, because I've very rarely been successful in presenting statistical evidence in a way that the court has understood or taken into account. There are so many ways in which statistics and probability can be misused, and only one which it can be used correctly, and that is the problem. And most people who haven't got the training, and even some of those who have, I can't really distinguish the good from the bad uses. So in Britain, and I'm sure in many places, its become standard for expert witnesses, forensic scientists to express their evidence in the form of a likely ratio, comparing the probability of certain evidence under two or even more hypotheses. And I think that is, in general, very good advice, because it does try and crystalize the semi-objective aspects of the evidence. And leave it to the trier of fact, the judge, the jury, to search formally or informally their own prior opinions and their reaction to other evidence. Now, they take account of that. But there are a number of cases where that too, is problematic. I don't think there's a simple answer. Sometimes prior probabilities involving, without any evidence, what is the chance of the person in front of you in the dark? Could have been the perpetrator cannot be ignored and even if it's, should not be quantified to precisely, I do think that it has to be discussed and taken into account. >> Thank you very much, Phil. >> Right. >> The second point I will like to underline in the analysis of this case is the need to refer to ratio of probabilities and not to a single probability, for example, the probability of observing to see the death. Why do we need this ratio? Because at trial, it has been suggested that the tiny probability for naturally occurring deaths is 1 in 73 million, constituted strong, say very strong evidence against Sally Clark and supported guilt. For Sally Clark, if the jury accepted that there was only 1 in 73 million probability that the two deaths occurred due to SIDS, it was an easy but fallacious step to conclude there was a 1 in 73 million chance that Mrs. Clark was guilty of murder. The complement of this probability, say 1 minus 1 in 73 million, was equated to the probability of murder. And the relevant question put forward by Professor Darwit is not what is the probability that these deaths were natural? But is it more likely that these deaths were natural rather than deliberate? In order to answer this question, it also would have needed to assess the probability of the alternative explanation of a mother murdering her two children. And to compare that with the probability of two natural deaths. In his wrapper Professor Phil Darwit, pointed out some statistics for infants murdered in England and Wales in 1996, and suggests that the probability of two babies in one family being murder was approximately 1 in 2 billion, a values much lower than 1 in 73 million. It showed that the two deaths are more probable under the hypothesis of SIDS than under the alternative hypothesis of murder. >> If any weight should be assigned to the evidence constituted by these two deaths, it should favor the SIDS hypothesis, versus the murder hypothesis. It gives a complete different perspective to the value of 1 in 73 million used by the prosecution. So in conclusion, we can say that extreme care should be exercised with any probabilistic calculations or presentation of such value. Statistical figures can have undue impact, notably, in front of a court. In this video, we have seen that we must not multiply the probability of events that are not independent. As you remember, probabilities depend on what we know. And if we know that had been another event, for example the first death that happened suddenly, this impact probability observing the second death. Also, it is crucial to display or disclose the source of data, in order to be transparent and to give our assumptions. For example, that the evidence are independent. This is an essential point that can also be found in the guideline and should be closely monitored. The last point is that as we have seen multiple times, that it is of paramount importance to consider the ratio of two probabilities. A way to do it, and in order to be balanced, we need to consider the ratio of the probability of the results given the prosecution and given the defense proposition. This is what is described as the likelihood ratio in the guideline. Undo assumption of independence between Evans, and misinterpretation of the meaning of a numerical value are recurrent problems in written and oral expert evidence presentation. To avoid such misinterpretation, care, education and auditing is needed. Another recurrent challenge is to check whether scientists gave an opinion on the results or on propositions. In the Sally Clark case, should the scientists, for example, give their opinion on what is the probability that these deaths were natural, or give their opinion on the result of the autopsy, given that these deaths were natural. We know, then the scientist needs to address the latter, while statistician may hold the court in addressing the proposition themselves. So we'll see additional example on these precise aspect, but this time involving DNA in the next part of this week. >> Thank you for watching. [MUSIC] [MUSIC]
