Some myths concerning statistical hypothesis testing
Robert Dodier
robert_dodier at yahoo.com
Tue Nov 12 22:24:44 EST 2002
Sturla Molden <sturla at molden_dot_net.invalid> wrote:
> On Sun, 10 Nov 2002 17:08:24 +0100, Robert Dodier wrote:
>
> > Now, computing the solution may be extremely difficult -- generally
> > involving multidimensional integrations. However, at least you can see
> > where you're headed -- there is a ``right answer'' to work towards.
>
> Markov chain Monte Carlo methods such as the Gibbs sampler
> is a handy tool for computing such integrals. In general
> we are interested in a number, so we don't need to obtain
> analytic solutions. Numerical methods also alleviate the
> need for conjugate priors. [...]
Well, I think there is still room for developing a greater range
of symbolic solutions, so that numerical solutions don't need to
come into play as often.
The methods mentioned above (Markov chain Monte Carlo) are very
general, but are not very efficient. Running for hours or days to
make a single calculation is not out of the question.
The strategy which seems most profitable to me is to identify
problems for which exact results are known, and then try to automatically
match a new problem with the catalog of known results, and only fall
back on numerical methods as they become necessary.
One symbolic result is worth a billion crunched numbers, in my
rough estimate. Now, if only I were better with calculus!
For what it's worth,
Robert Dodier
--
``He wins most who toys with the dies.'' -- David O'Bedlam
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