- On 1 Oct 2000 at 22:15:36, "Genshin TEI" (tei.-a-.yo.rim.or.jp) sent the message

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Dear all

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

Bayesian approach.

The following is what the ECONOMIST magazine in London wrote:

http://www.economist.com/

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.

Previous convictions

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

rise.

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

quickly.

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

Reply to.... genshin.tei.-a-.nifty.com

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