Re: Error on kurtosis and skewness

Jerry Dallal wrote:
> I hate to deflect someone from what looks like a profitable endeavor
> and, unfortunately, Reef Fish is gone for a few days so he can't comment
> on whether it might be too soon for you, but, given the kinds of
> questions you like to ask, you might *really* enjoy looking at
> comparative statistical inference--for example, comparing the
> frequentist and Bayesian approaches (and, decision theoretic, as
> Professor Rubin might add, which still leaves schools unmentioned) to
> statistics.

I have looked at this a little bit, but must admit that I was mystified
at some of the distinctions. When I've seen definitions of what a
"Bayesian" is, they have fitted my own attitudes to such a degree that
the main problem I have is understanding why someone would believe
otherwise. In particular, the incorporation of prior belief in
reasoning. In AI we expect beliefs of an agent to be "rational".
"Rational" is an ill-defined concept, but if there are strong reasons
to believe one side of a hypothesis ahead of time, such as a belief
that homeopathy is hogwash given that homeopathy working would
contradict too much other knowledge that is on firm ground, then I
believe that it is rational to expect a very different standard of
evidence before changing that belief to one that homeopathy works for
the reasons that its proponents claim it does. To require the same
standard of evidence for the hypothesis that one flavour of chewing gum
is outselling another flavour is, in my world-view, irrational.

[rambling rant on my views on AI and why I frequent this newsgroup
deleted]

> Where the frequentist has CIs and is unable to attach probability
> statement to them, the Bayesian has "credible intervals" and is
> *allowed* to say things like "the probability that the mean lies between
> 2.6 and 7.3 is 95%".

Yes, I was thinking that myself. As you said, the interval either
contains the value for theta or it doesn't. However, the first thing
that popped into my mind was that if we have to put some sort of
probability on the value of interest being within the interval so that
some decision can be made, what other probability or alternative
measure of belief can we choose? We can only live our lives reasoning
with the knowledge we have, not that we don't :-)

The advice about the robust stats book is appreciated. Unfortunately
for the advice to take effect, it requires me to be sensible and act in
a logical and efficient manner. And, sadly I don't work that way and
I've given up on ever trying. And, I've found that I seem to make
better progress just going with the flow than planning. Digging down in
my desk I find I have _Introduction to Probability Theory_ by
Hoel/Port/Stone here. As far as I can see from a quick flick through,
having a go at reading it can't do me any harm. If I get stuck, I can
always put it down and pick up another book. My library card is always
right on the loan limit, and I can't read all of those at once.

BTW: I have actually reviewed the argument I had with Reef Fish on
Multidimensional Scaling. Not from the point of view of continuing it
or contesting any points, but from the point of view of considering
what went wrong with a discussion that started quite well. If I had
been sensible and logical, the arguments would never have happened, but
that's life. As it turned out, the difficulties I was having vanished
when I stopped arguing and read the next chapter in my book.

Cheers,

Ross-c

.

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