= Error exponents in hypothesis testing
{title2=$E=\lim_{n\to\infty}-n^{-1}\log p_n$}
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= Error exponent
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An error exponent is the limiting exponential decay rate of an error probability $p_n$ as sample size $n$ grows. Different constraints on the <Type I error> and <Type II error> give different optimal rates. The <Chernoff information> describes the optimal average-error rate for simple Bayesian hypotheses; <Stein's lemma (information theory)> gives the optimal type-II rate when type-I error is held below a fixed nontrivial bound.
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