By Topic

Maximum entropy and conditional probability

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)

It is well-known that maximum entropy distributions, subject to appropriate moment constraints, arise in physics and mathematics. In an attempt to find a physical reason for the appearance of maximum entropy distributions, the following theorem is offered. The conditional distribution of X_{l} given the empirical observation (1/n)\sum ^{n}_{i}=_{l}h(X_{i})=\alpha , where X_{1},X_{2}, \cdots are independent identically distributed random variables with common density g converges to f_{\lambda }(x)=e^{\lambda ^{t}h(X)}g(x) (Suitably normalized), where \lambda is chosen to satisfy \int f_{\lambda }(x)h(x)dx= \alpha . Thus the conditional distribution of a given random variable X is the (normalized) product of the maximum entropy distribution and the initial distribution. This distribution is the maximum entropy distribution when g is uniform. The proof of this and related results relies heavily on the work of Zabell and Lanford.

Published in:

IEEE Transactions on Information Theory  (Volume:27 ,  Issue: 4 )