Chance news 2.12 
               (18 June to 4 July 1993)

Prepared by Laurie Snell

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>>>>>==========>> The big news this week was the solution to Fermat's last problem You might think that this has little to do with chance but don't forget that Fermat was a co-founder of probability and so we should be pleased that he was proven correct after all these years. Also there are a lot of bets on whether or not the proof is correct. <<<========<<

>>>>>==========>> Also in the news was the letter to Ann Landers complaining about the mathematicians who wasted a lot of time and government money trying to find the smallest number of people that you can invite to a party to be sure that there are either a group of four who are totally unacquainted or a group of five that are completely acquainted. (The letter said "and" instead of "or" getting the problem slightly wrong.) To make this Chance news we recall that Paul Erdos uses probability to study these Ramsey numbers. He gets a lower bound for the number you need to invite as follows: If you have n people, choose a random graph by connecting each pair of points with probability p. Then for a particular four people to be completely acquainted 6 lines must be connected and the probability for this is p^6. For a particular five people to be totally unacquainted ten pairs of points must not be connected and the probability for this is (1-p)^10. Thus the expected number of favorable subgraphs is (n choose 4)*p^6 + (n choose 5)*(1-p)^10. If this is less than 1 there must be some graph with no favorable subgraph and so this value of n is not big enough. Using this result we can see that there is a value of p that makes the expected value < 1 for values of n up to 8. Thus we must invite at least 9 people. Eleven years of computing time showed that in fact you must invite at least 25 and if you do invite 25 you will be successful. <<<========<<

>>>>>==========>> From Bill Peterson. Recognizing Handwriting in Context. Science 18 June 1993, p. 1723. David H. Freeman The best computerized handwriting recognition systems available today are able to recognized roughly half of the words they are presented. Conventional systems work by guessing each letter of a written word based on analysis of lines and curves. A new system, developed at the Univ. of Buffalo, works in tandem with conventional systems. It picks the best word from a set of alternative based on which alternative is most likely from a grammatical standpoint to appear next in the sentence. The system relies on a set of probabilities known as "statistical grammar." The probabilities were derived from a statistical analysis of e-mail messages (which are expected to exhibit the same level of informality as handwritten messages). Other researchers are applying similar techniques to character recognition, structuring searches via what letters most likely to follow a given letter. This approach leads to what is called a hidden Markov Chain. The text itself is assumed to be a Markov Chain but when this Markov Chain is in a given state the writer produces another random process in a scribbly attempt to produce the letter and this is the process that is observed. <<<========<<

>>>>>==========>> Experts say many treated for Lyme disease don't have it. Dallas Morning News, 18 June, 1993, 1A Laura Beil Conditions such as depression, chronic fatigue, aching muscles mimic Lyme disease and the recent publicity of this disease has led many people to ask for and often receive treatment for Lyme disease who, in fact, don't have it. The treatment is expensive and also giving high doses of antibodies can lead to complications. More reliable tests are needed for the presence of the disease and more studies to test ticks to determine the degree of infestation in a given area. <<<========<<

>>>>>==========>> Whether positive or negative, result of prostate cancer test can create maze of questions. The New York Times, 23 June 1993, C12 Gina Kolata More discussion about the controversy surrounding the use of the PSA test for prostate cancer. The incidence of prostate cancer is second only to lung cancer in men. Autopsy studies have shown that half of the men over 50 have cancerous cells in their prostates but only about 2.4% die from prostate cancer. Both the false positive and false negative rates are high for the PSA test. When a person tests positive there are more tests to do and these are often not conclusive. This, combined with the fact that, even if a person has the cancerous cells it may never cause a serious problem, leaves the patients with difficult decisions to make. The doctors have difficult decisions also since it is discouraging to have patients dying who could have been saved by an early diagnosis. As a result some doctors argue that PSA testing should not be done until there is data showing it saves lives while other recommend it on an annual basis. <<<========<<

>>>>>==========>> Judges get broader discretion in allowing scientific testimony. Washington Post, 29 June, 1993, A6 Joan Biskupic The supreme court has made its first ruling in its history on how courts should use scientific evidence. The judges discarded the 1923 Frye test that said that scientific evidence should have general acceptance in the relevant scientific field saying that the Federal Rules of Evidence in 1975 replaced the Frye test. Under the latter rule, "If scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, or experience, training, or education may testify thereto in the form of an opinion or otherwise". The court said that Federal judges should use their judgment based upon an understanding of the way that scientific theories are evaluated to determine the admissibility of scientific evidence. Peer review is not required but is an important part of such evidence as is reproducibility of results etc. Of course, the judges job is to just rule out junk science and it will still be up to the jury to evaluate the force of the scientific testimony. It is hoped that this will clarify some of the controversy over issues such as the use of DNA fingerprinting in the courts. It was easier for a judge to not allow DNA fingerprinting under the Frye criteria than it will be under the Federal Rules of Evidence. <<<========<<

>>>>>==========>> Electrical emissions: dangerous or not? The New York Times, 22 June, 1993, C1 Gary Taubes A long article reviewing the debate over whether electromagnetic fields can cause childhood cancer. The article discusses the difficulties of basing a positive conclusion on epidemiology studies that indicate only a small effect, if any, and are sometimes even contradictory. The difficulty in inducing or promoting cancer in animals using low-level electromagnetic fields is described as a biological argument against the causal effect. Also from a physical point of view, it is argued that the magnetic field from the earth is 200 to 300 times as great in the United States as the levels from power lines and appliances so why worry about these relatively small fields. This article seems to want to reassure the public that this is probably not a problem. However, it does state that the utility companies are spending a billion dollars a year to reduce exposure and are preparing to face additional lawsuits. <<<========<<

>>>>>==========>> Experts change guides to using drugs for H.I.V. The New York Times, 27 June, 1993, A23. Lawrence K. Altman The National Institutes of Health has issued new guidelines for treating people infected with the H.I.V. virus. These guidelines are more flexible than the old ones, reflecting the influence of the recent European study showing that early treatment with AZT is less effective than had been previously believed. Current medical practice has been to give AZT routinely to patients whose have not yet shown symptoms but have an C4 count below a certain level. This is changed to recommend that the decision when to start AZT be made by the doctors with their patients with a complete discussion of the benefits and the risks. The European study did not say anything about the value of AZT therapy after AIDS developed. Also the committee had little data to help in a recommendation for those who did start early as to whether they should continue or not. For those with progressive AIDS symptoms despite the use of AZT, the panel recommended switching to ddI. <<<========<<

>>>>>==========>> The search for proof. The Seattle Times, 29 June, 1993, E1 Carey Quan Gelernter Like the question of the dangers of electromagnetic fields the controversy of the benefits of mammography for women between 40 and 50 centers around the validity of the recent studies that suggest that mammograms are not helpful for this age group. The article discusses the economic factors that prevented these studies from being more conclusive and the studies under way to try to remedy this. They refer to a study just being completed which purports to show that these new studies under way, as large as they are, are not large enough to settle the issue. There will be an international conference in Geneva in September to look at a meta-analysis but the article says that there is a fair degree of pessimism over the possibility of settling anything by these methods. <<<========<<

>>>>>==========>> Even experts disagree on mammograms accuracy. The Seattle Times, 29 June, 1993, E1 Carey Quan Gelernter A Yale University study investigated the consistency of 10 experienced radiologists in evaluating high-quality mammograms taken in 1987. While the study has not been published, a brief discussion of the results is provided in a recent issue of the Journal of American Medical Association. The studied found that the experts disagreed in a third of the cases on whether the women had cancer, and a quarter of the time on recommended follow-up (such as biopsy or additional mammograms). In addition they often reached a different conclusion when examining the same X-rays five months later. This article discusses some of the reasons for the difficulties in getting consistent results and some of the remedies under consideration for this problem. <<<========<<

>>>>>==========>> Can statistics tell us what we do not want to hear? The case of complex salary structures. Statistical Science Vol.8 No.2, May 1993 Mary W. Gray The author (a statistician and lawyer) puts forth the thesis that the main use of statistics is to bolster the decisions of policy makers to make decisions that they were prepared to make on other grounds. She suggests that when statistics does not tell them what they want to hear, they are inclined to not listen to it. She illustrates this idea briefly in terms of the familiar issues of the use of SAT scores, DNA fingerprinting in the courts, secondary effects of smoking etc., and then, in depth, in terms of the use of statistics in the courts to settle issues of discrimination on the basis of race, sex, national origin or religion. Gray presents an analysis of a number of actual cases showing the many difficulties involved in applying a statistical analysis, usually in terms of multiple regression, to an issue like salary discrimination. Her expertise and experience both as statistician and lawyer makes this a fascinating discussion. Obviously, many of the problems in this application of multiple regression are relevant to other kinds of applications. The article is followed by discussions of other who provide other examples and insights into using statistics in discrimination cases. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Chance news 2.12 (18 June to 4 July 1993) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu >>>==========>>|<<==========<<<