Consider a weather forecaster predicting the probability of rain for the next day. We consider tests that given a finite sequence of forecast predictions and outcomes will either pass or fail the forecaster. It is known that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. This note summarizes and examines the computational complexity of such forecasters.
/lp/association-for-computing-machinery/the-complexity-of-forecast-testing-76ppqMVNa5