Welcome to this new video. Well, the Sally Clark case can be summarized as follows. One evening in December 1996, Sally Clark was alone at her home with her first-born son, Christopher, age of two and a half months, when till then was a healthy child. Two hours after his early evening feed, his mother found him apparently dead in his bouncy chair, and called the ambulance. Resuscitation was unsuccessful. The conclusion of a postmortem pathologist examination was that the death was due to a lower respiration tract infection, probably sudden infant death syndrome or SIDS. In January 1998, Sally's second child, Harry, died, aged two months, in almost identical circumstances. Both parents were, at that time, in the house. Because of the previous unexpected death, their second child was still subject to intensive medical monitoring. The postmortem examination found signs of recent bleeding at the back of the eyes and in the spinal cord. His death was treated as suspicious by the pathologist, and he also revisited the death of a first child and determined that the first two was suspicious. The parents were both suspected, but soon the police focused on Sally Clark. She was arrested and accused of having murdered her two children by smothering. There were no witness to the actions Sally Clark was accused of. What is the evidence, and why statistics play the role against her? The evidence against her consisted of information provided by a list of qualified medical expert called by the prosecution. The expert called by the prosecution look at the medical evidence available to the report, such as the autopsy for both babies, and state that this provide that both death were caused deliberately either by shaking or smothering. Since Sally Clark was the only person with each child when they died, the evidence points to her. The expert for the defense argued that the evidence was not conclusive and that the cause of both death were unclear. Sally Clark was initially convicted of murdering both children and received two-life sentences. In 2000 and 2003, she appealed to the Court of Appeal. The Court of Appeal, in both cases, did not object fundamentally to the statistical argument, but didn't feel it was useful. In 2000, they said, "The one in 73 million figure is no help. It is merely a distraction." In 2003, I quote, "If there had been a challenge to the admissibility of the evidence, we would have thought that the wisest course would have been to exclude it altogether." From a statistical point of view, however data used to support the prosecution. We will use here the statement produced by Professor Phil Dawid, at the time, Professor of Statistics at the Department of Statistical Science at the University College of London. He acted as defense expert in the appeal and argued against prosecutor expert who state that it was extremely rare to have two infants deaths occurring from unexplained natural causes in a family such as the Clark's. Later in a Skype interview, you will have the opportunity to hear Professor Dawid comment on this case. Using figure from an epidemiological study of the incidence of sudden infant death syndrome, the medical expert, a pediatric professor, claimed that the overall incidence of SIDS was one in 3,000 births, falling to about one in 8,500 if one took into account various characteristics of this family, the Clark family. For example, the fact that they are non-smokers and the mother was over 26 years old. The prosecution expert testify that the probability of a repeat occurrence, once a first SIDS death has appeared, would be essentially the same as the first. This would imply then that the probability of the two SIDS death, in the family like the Clark's, could be calculated by multiplying one in 8,500 by itself. This gives the final figure of one in 73 million for the probability of two SIDS death. No serious defense cross-examination was performed at the first trial on this statistical aspect. So, Franco, what is the problem? There are mainly two aspect we have to discuss. The first is related to the aspect of independence of an event. The second to the need to refer to ratio of probability and not single probability so to avoid fallacies pitfalls of intuition. Let us first illustrate the independence aspect. In probability, one of the law is that we can multiply the probability of events, say, A and B, when they are independent. For example, if we take the two events or the two proposition, Christophe has his birthday today and I have my birthday today, these two events are independent, so that the probability of Christophe having his birthday today and the probability of having my birthday today can be multiplied. We can multiply the probability because the two events do not depend on each other or on the common factor. But the probability of me filming in this room today and the probability of Christophe filming in this room today cannot be multiply because these two events depend on each other. In the case of SIDS in a family, one know that if a child has died of SIDS, then the probability of having another SIDS in this family is higher, than if it is the first time. Therefore, to calculate the probability of two SIDS deaths in the Clark family, we cannot, without justification, simply square the probability of a single death. It could be only done if we could reasonably argue for the independence of the two deaths. This means that after assigning the appropriate probability of one SIDS to the death of their first child, for sake of illustration, accept a value of one in 8,500, the same figure will apply to the death of the second, even after taking into account different deaths. This sound implausible because the two children must have shared many characteristics such as genetic features. Right. So, in fact, the first death gives reasons to believe that there might be some factors affecting both children, and that will increase the probability that the second child would be affected too. It reminds me similar criticisms on the independence assumptions in previous criminal cases. Take, for example, the Collin's case in California in the 60s. Alex will briefly talk about it. It is right that what happened in the Clark's case is not a new misuse of statistical data. The aim of this video is to discuss a famous case of misuse of statistics in forensic science, this time in the United States. In June 1964, Juanita Brooks was pushed to the ground as she walked down an alley in the San Pedro area of Los Angeles. According to Mrs. Brooks, a blonde-haired woman, dressed in dark clothing grabbed her purse and runaway. John Bass, who lived at the end of the alley, heard the incident and saw a blonde-haired woman wearing a dark clothing run from the scene. He also noticed that the woman had a ponytail and that she entered a yellow car driven by a black man who had a beard and a mustache. On the basis of this description, the police identified Janet and Malcolm Collins as suspect and charged them with robbery. At trial, the prosecutor called a professor of mathematics who testified about the product rule in probability theory. The probability that a series of independent events will occur is the product of the probabilities of each of the individual events. The prosecutor assigned a series of individual probabilities to the series of characteristics of the perpetrators as presented here. The six characteristics of the aggressors that have been mentioned are the following: a partly yellow car with probability of one in 10; a man with a mustache, one in 4; a girl with a ponytail, one in 10; a girl with blonde hair, one in three; a black man with a beard, one in 10; and an interracial couple in a car, one in 1,000. By multiplying the individual probabilities, it was claimed that the probability that a couple would have all six characteristics was one in 12 million. As you can imagine, several statistical problems arose in this case as, for example, where did the values come from or what was the interpretation of this final value. At the moment, we are only concerned with the aspect of independence. Do you think that a black man with a beard has the same probability to have a mustache as a black man without a beard? Are these characteristics independent? If an expert is to adopt such a strong independence assumption, it would be expected to disclose the appropriate data to support that view. In Collins, that was not the case, and the prosecution asked to blindly trust that assumption. These shortcoming didn't pass unnoticed. The Supreme Court of California identified the lack of justification of this independent assumption adopted by the prosecution in this case. Thank you for watching this video. You can follow us in the next video.