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Next year is the 300th anniversary of birth of Reverend Thomas
Bayes, an 18th-century Presbyterian minister and mathematician.
As you all know, we use the =93Bayesian" methods in PK/PD fields.
It's not a bad idea that we'd re-think over the essence of the
The following is what the ECONOMIST magazine in London wrote:
How do you think ?
(c)The ECONOMIST, Sep 30th - Oct 6th, 2000.
IN PRAISE OF BAYES
BAYESIANISM IS A CONTROVERSIAL BUT INCREASINGLY
POPULAR APPROACH TO STATISTICS THAT OFFERS
MANY BENEFITS---ALTHOUGH NOT EVERYONE IS
PERSUADED OF ITS VALIDITY
IT IS not often that a man born 300 years ago suddenly springs back to
life. But that is what has happened to the Reverend Thomas
Bayes, an 18th-century Presbyterian minister and mathematician-in spirit,
at least, if not in body. Over the past decade the value
of a statistical method outlined by Bayes in a paper first published in
1763 has become increasingly apparent and has resulted in a
blossoming of =93Bayesian" methods in scientific fields ranging from
archaeology to computing. Bayes's fans have restored his tomb
and posted pictures of it on the Internet, and a celebratory bash is
planned for next year to mark the 300th anniversary of his
birth. There is even a Bayes songbook-though, since Bayesians are an
academic bunch, it is available only in the obscure file
formats that are used for scientific papers.
Proponents of the Bayesian approach argue that it has many advantages
over traditional, =93frequentist" statistical methods.
Expressing scientific results in Bayesian terms, they suggest, makes them
easier to understand and makes borderline or inconclusive
results less prone to misinterpretation. Bayesians claim that their
methods could make clinical trials of drugs faster and fairer,
and computers easier to use. There are even suggestions that Bayes's
ideas could prompt a re-evaluation of fundamental scientific
concepts of evidence and causality. Not bad for an old dead white male.
The essence of the Bayesian approach is to provide a mathematical rule
explaining how you should change your existing beliefs in the
light of new evidence. In other words, it allows scientists to combine
new data with their existing knowledge or expertise.
The canonical example is to imagine that a precocious newborn observes
his first sunset, and wonders whether the sun will rise again
or not. He assigns equal prior probabilities to both possible outcomes,
and represents this by placing one white and one black
marble into a bag. The following day, when the sun rises, the child
places another white marble in the bag. The probability that a
marble plucked randomly from the bag will be white (i.e., the child's
degree of belief in future sunrises) has thus gone from a half
to two-thirds. After sunrise the next day, the child adds another white
marble, and the probability (and thus the degree of belief)
goes from two-thirds to three-quarters. And so on. Gradually, the initial
belief that the sun is just as likely as not to rise each
morning is modified to become a near-certainty that the sun will always
In a Bayesian analysis, in other words, a set of observations should be
seen as something that changes opinion, rather than as a
means of determining ultimate truth. In the case of a drug trial, for
example, it is possible to evaluate and compare the degree to
which a skeptic and an enthusiast would be convinced by a particular set
of results. Only if the skeptic can be convinced should a
drug be licensed for use.
This is far more subtle than the traditional way of presenting results,
in which an outcome is deemed statistically significant only
if there is a better than 95% chance that it could not have occurred by
chance. The problem, according to Robert Matthews, a
mathematician at Aston University in Birmingham, is that medical
researchers have failed to understand that subtlety. In a paper to
be published shortly in the Journal of Statistical Planning and Inference,
he sets out to demystify the Bayesian approach, and
explains how to apply it after the event to existing data.
Patients in clinical trials will soon benefit. Bayesian methods offer the
possibility of modifying a trial while it is being
conducted, something that is impossible with traditional statistics. Andy
Grieve and his colleagues at Pfizer, a drug firm, are
intending to do just that.
Traditionally, dose-allocation trials-in which the aim is to establish
the most effective dose of a new drug-involve giving
different groups of patients different doses and evaluating the results
once the trial has finished. This is fine from a statistical
point of view, but unfair on those patients who turn out to have been
given non-optimal doses. Rather than analyzing the results at
the end of a trial, Dr Grieve's method will evaluate patients'
responses during it, and adjust the doses accordingly. The
advantage of this over the traditional approach that it maximizes the
medical benefit to all participants. It also means that fewer
people are needed to conduct a trial, because participants on non-optimal
doses can have those doses changed to increase the amount
of data collected near the optimal dose.
Pfizer is intending to conduct a trial using this new method, and the
plan is to re-analyze the data once it is completed in ways
that will satisfy both Bayesians and non-Bayesians. This kind of parallel
approach is likely to become increasingly common, at least
until Bayesianism has been more widely accepted.
Bayesian methods can also be used to decide between several competing
hypotheses, by seeing which is most consistent with the
available data. This idea was recently used to determine the date of
construction of =93Seahenge", an ancient timber circle found
off the coast of Norfolk, in eastern England. Results from tree-ring
dating were inconclusive, suggesting such divergent dates as
2019BC, 2050BC and 2454BC. So six samples from the monument's central
stump were radiocarbon-dated, and the results were used to
evaluate the three tree-ring possibilities via Bayesian analysis. The
evidence was overwhelmingly in favour of 2050BC, and was
inconsistent with either of the other two tree-ring dates.
Decision-making using Bayesian methods has many applications in software,
as well. Perhaps the best-known example is Microsoft's
Office Assistant, which appears as a somewhat irritating anthropomorphic
paper-clip that tries to help the user. When a user calls
up the assistant, Bayesian methods are used to analyze recent actions in
order to try to work out what the user is attempting to do,
with this calculation constantly being modified in the light of new
actions. (Unfortunately, a non-Bayesian approach is used to
decide when to make the paper-clip pop up on its own, adding to the
annoyance of many users.) According to Eric Horvitz, a
statistician in Microsoft's research division, future products will try
to determine users' intentions more broadly, so as to
speed things up. Having worked out which link on a web article a user is
most likely to click on, for example, the computer could
fetch the corresponding article in advance, so that it appears more
Bayes is still, however, the focus of much controversy. Larry Wasserman,
a statistician at Carnegie Mellon University, in Pittsburgh, says that
although Bayesianism is becoming more acceptable,
it is no panacea, and when used indiscriminately it becomes
"more a religion than a science". Perhaps the grandest claims made for
Bayesian methods are those of Judea Pearl, a computer
scientist at the University of California, Los Angeles. Dr Pearl has
suggested that by analyzing scientific data using a Bayesian
approach it may be possible to distinguish between correlation (in which
two phenomena, such as smoking and lung cancer, occur
together) and causation (in which one actually causes the other).
This kind of claim makes many scientists, including many
Bayesians, throw up their hands in horror. Evidently there is life in the
old reverend yet.
Genshin TEI, RPh. Chief Pharmacist
Osaka Prefectural General Hospital
Osaka City, JAPAN
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Copyright 1995-2010 David W. A. Bourne (firstname.lastname@example.org)