Maximum entropy and conditional probability

摘要: It is well-known that maximum entropy distributions, subject to appropriate moment constraints, arise in physics and mathematics. In an attempt find a physical reason for the appearance of following theorem offered. The conditional distribution X_{l} given 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 f_{\lambda}(x)=e^{\lambda^{t}h(X)}g(x) (Suitably normalized), \lambda chosen satisfy \int f_{lambda}(x)h(x)dx= \alpha . Thus variable X (normalized) product initial distribution. This when uniform. proof this related results relies heavily on work Zabell Lanford.