Entropy Maximization

Proceedings Mathematical Sciences

K B Athreya¹ 

[1] Department of Mathematics and Statistics, Iowa State University, USA$$

关键词: Entropy;    relative entropy;    entropy maximization.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf 𝑓 that satisfy $int fh_id_𝜇=𝜆_i$ for $i=1,2,ldots,ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $exp(sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.

【 授权许可】

Unknown