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Chance news 2.12
(18 June to 4 July 1993)
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Prepared by Laurie Snell
Please send suggestions for articles or format to
dart.chance@dartmouth.edu
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"What is needed is to bring the cold numbers convincingly to
life" (International Brotherhood of Teamsters V. United States)
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ARTICLES ABSTRACTED
>>>>>==========>> 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Chance news 2.12
(18 June to 4 July 1993)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu
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