談模式好壞和對錯 (David Kerridge)

Dear Hanching,

Thanks for the information about Joyce Orsini's forthcoming book, and
the review of the book on Bayes Theorem.

I think that there is a lot more to be discovered about Bayes Theorem.
It is certainly a very important practical tool. For example, my email
is scanned for spam by a programme based on Bayes Theorem. But I rather
suspect it is not being used correctly - and still works.

In 1964 I was a Research Fellow, and two of us were investigating
methods of medical diagnosis. In other words, trying to develop
statistical rules for guessing what illness a patient is suffering from,
based on a limited number of tests or symptoms.

We found a paper, written by a computer scientist, that claimed to use
Bayes Theorem in medical diagnosis. But his method did not allow for the
obvious fact that different symptoms are not statistically independent.

We were shocked at such ignorance, and misuse of statistical theory. So
we set out to compare all the best methods we could find, including new
ones we developed ourselves, based on multivariate logistic analysis,
and another based on comparing each case with all the data in a
database.

Sad to say, the "wrong" method, based on bad theory, worked at least as
well as the other methods, though which worked best, for a particular
disease, depended on the sample size available. Ours was better for
large samples.

It seems that a simple, even a wrong model, can equal or sometimes beat
a better model with fewer parameters. I later found out that Norman
Bailey, at Oxford, had discovered the same thing in a different problem
(multiple regression), but found it so shocking that he did not publish
it.

The point I am making is that "correct theory" does not guarantee better
results in practice, and vice versa. Statistical theory hasn't caught up
with this fact yet, as far as I know.

I will try to explain the difference between the way Sir Harold Jeffreys
and W Edwards Deming *used* probability, which tells you more than what
they say. But it will take time, as I like to be thorough.

David