Chernoff information is related to the optimal Bayes error of misclassifying observations based on a 2-class hypothesis.
It is related to the likelihood ratio test.
For two probability measures, the Chernoff information is defined as
C^*(p_1,p_2) = C_{\alpha^*}(p_1,p_2)= -\log \min_{\alpha\in (0,1)} \int p_1^{\alpha}(x)p_2^{1-\alpha}(x) \mathrm{d}x \geq 0.
Best achievable exponent for a Bayesian probability of error.
The probability of error of the nearest neighbour rule for classification is upper bounded by twice the Bayes error.
History
The statistical measured appeared in
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
Herman Chernoff
Ann. Math. Statist. Volume 23, Number 4 (1952), 493-507.
The paper is available here (courtesy of JSTOR).
The formula explicitly appears in Section 7, page 507:
© 2010 Frank Nielsen.