Title: De Finetti, Hausdorff, and the Markov moment problem

Speaker: David Freedman

Abstract:

The Markov moment problem is to characterize sequences that
are moments of a probability density bounded above by a given
positive constant. There are characterizations by the Russian
school through complex systems of non-linear inequalities.
Necessary and sufficient linear conditions were given by
Hausdorff, in terms of an auxiliary doubly-indexed array
whose (n,j)th entry turns out to be the probability of j heads
in n tosses for an associated coin-tossing game.  This is de
Finetti's theorem in disguise. I will give some new proofs with
ancillary results, for example, characterizing prior opinions
about coin-tossing when there is a monotone density.  This
is joint work with Persi Diaconis.  The overheads are on
the web,

           http://www.stat.berkeley.edu/~census/momilan.pdf

So is the paper,

           http://www.stat.berkeley.edu/~census/631.pdf