I have a series $x_n$, for $n=1,\dots,N$, with $x_0<0$ and and $x_N>0$. For each $n$, I can test whether $x_n>0$, which gives me a probability $p$ that $x_n>0$. If $p\in\{0,1\}$, I would use a the bisection method. How can I extend this to the probabilistic case?
This question is similar to Root finding for stochastic function, which deals with finding roots in a continuous interval (say [0,1]).
