## A first minimax lower bound in the two hypothesis scenario

Photos of  Johann Radon and Otto Nikodym. Sources: Apprendre les Mathématiques and Wikipedia. Consider the simplest case, $latex {M=1}&fg=000000$ with two hypothesis $latex {\{f_{1},f_{2}\}}&fg=000000$ belonging to $latex {\mathcal{F}}&fg=000000$. According to the last post, we need only to find lower bounds for the minimax probability of error $latex {p_{e,1}}&fg=000000$. Today, we will find a bound using …