Chernoff's bound forms

Details Chernoff's bound forms Chernoff's bound forms

2003-06-23

arxiv.org/abs/math/0306326v1

In: Bayesian inference and Maximum Entropy methods in Science and Engineering, Ch. Williams (ed.), AIP (Melville), 67-72, 2003

Mathematics

Probability

M. Grendar, Jr. and M. Grendar, ``Chernoff's bound forms,'' in Bayesian inference and Maximum Entropy methods in Science and E

Scientific paper

10.1063/1.1570535

Chernoff's bound binds a tail probability (ie. $Pr(X \ge a)$, where $a \ge EX$). Assuming that the distribution of $X$ is $Q$, the logarithm of the bound is known to be equal to the value of relative entropy (or minus Kullback-Leibler distance) for $I$-projection $\hat P$ of $Q$ on a set $\mathcal{H} \triangleq \{P: E_PX = a\}$. Here, Chernoff's bound is related to Maximum Likelihood on exponential form and consequently implications for the notion of complementarity are discussed. Moreover, a novel form of the bound is proposed, which expresses the value of the Chernoff's bound directly in terms of the $I$-projection (or generalized $I$-projection).

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