[extropy-chat] A New Year's gift for Bayesians

[Amara Graps]

Eliezer S. Yudkowsky sentience at pobox.com :
>If we are to evaluate all events in the universe, how do we 
>compute the joint probability of all those events together?

I'm looking forward to Robin's answer on this, but I think that
either it doesn't matter what order you compute the joint
probability, or else you calculate it based on what you know of
the importance of the parameters.

"In a continuous multiparameter situations, there is no hope for
a single, unique "non-informative prior", appropriate for all the
inference problems within a given model. To avoid having the
prior dominating the posterior for _some_ function theta of
interest, the prior has to depend not only on the model, but also
on the parameter of interest or, more generally, on some notion
of the order of importance of the parameters."

Jose Bernardo, Adrian Smith, _Bayesian Theory_, Wiley, 2000, 
pg. 366.

Perhaps you've seen the papers where cosmologists are estimating
parameters from cosmic microwave background measurements. The
next paper, in particular, shows in detail how to constrain the
parameters on a grid using the Markov Chain Monte Carlo Methods,
which cuts down the computations considerably.

Amara

Nelson, Christensen, Rate Meyer, Lloyd Knox, and Ben Luey (2001),
"Bayesian methods for cosmological parameter estimation from
cosmic microwave background measurements", Class. Quantum Grav.
18, 2677-2688.


Amara Graps, PhD          www.amara.com
Istituto di Fisica dello Spazio Interplanetario (IFSI)
Istituto Nazionale di Astrofisica (INAF),
Adjunct Assistant Professor Astronomy, AUR,
Roma, ITALIA     Amara.Graps at ifsi.rm.cnr.it