[YPNG] YPNG Friday 12 October 2018 at 11:00-1:00, 24 Hillhouse Ave

[David Pollard]

Hi Folks,

This week we have the second in a series of talks by Xiaosheng Mu,
who is currently a postdoc at Cowles. (His first talk was in November 2012.)

Combining and comparing experiments

An experiment X Blackwell dominates another experiment Y if in every
decision problem, X leads to higher expected payoff/lower risk than Y
(Blackwell 1951, 1953). We study two related orders on experiments. Say
X is eventually better than Y if for all large N, N conditionally
independent copies of X Blackwell dominate N copies of Y. Say X is
marginally better than Y if there exists a third experiment Z such that
the product experiment of X and Z Blackwell dominates the product of Y
and Z. Using tools from large deviations/extreme value theory, we fully
characterize these eventual and marginal Blackwell orders in the case of
binary states. As an application, we prove that linear combinations of
KL divergences are the only cost functions of experiments that satisfy
Blackwell monotonicity, additivity w.r.t. taking product experiments,
and affinity w.r.t. mixing with the trivial experiment. Our techniques
also apply to the eventual and marginal comparisons of random variables,
in the sense of first or second order stochastic dominance. 



YPNG ps. Back in the olden days, good authors could say a lot in under ten pages:

Blackwell, David. Comparison of Experiments. Proceedings of the Second
Berkeley Symposium on Mathematical Statistics and Probability, 93--102,
University of California Press, Berkeley, Calif., 1951.
https://projecteuclid.org/euclid.bsmsp/1200500222

Blackwell, David. "Equivalent Comparisons of Experiments." The Annals of
Mathematical Statistics 24, no. 2 (1953): 265-72.
http://www.jstor.org/stable/2236332.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.yale.edu/pipermail/ypng/attachments/20181011/892a13ed/attachment.html>