<Stein's lemma (information theory)> states that for testing $P^{\otimes n}$ against $Q^{\otimes n}$, the smallest <Type II error> $\beta_n$ among tests with <Type I error> at most any fixed $0<\varepsilon<1$ satisfies
$$
\lim_{n\to\infty}-\frac1n\log\beta_n=D(P\Vert Q).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 224 / 1 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-224/1/a/solution