Neyman-Pearson lemma

Named after Jerzy Neyman and Egon Pearson, who published the result in 1933 [1], the Neyman–Pearson lemma can be considered as the theoretical cornerstone of the modern theory of hypothesis testing. Although the situation it is addressing (a simple null hypothesis versus a simple alternative) is of limited practical value, this lemma paved the way for all further developments of the theory; see Ref. [2] for an overview. We briefly state that fundamental result, and describe some immediate applications to standard one-sided one-parameter problems.