A Genetic Algorithm-based Framework for Learning Statistical Power Manifold

Statistical power is a measure of the goodness/strength of a hypothesis test. Formally, it is the probability of detecting an effect, if there is a true effect present to detect. Hence, optimizing statistical power as a function of some parameters of a hypothesis test is desirable. However, for most hypothesis tests, the explicit functional form of statistical power as a function of those parameters is unknown but calculating statistical power for a given set of values of those parameters is possible using simulated experiments. These simulated experiments are usually computationally expensive. Hence, developing the entire statistical power manifold using simulations can be very time-consuming. Motivated by this, we propose a novel genetic algorithm-based framework for learning statistical power manifold. For a multiple linear regression $F$-test, we show that the proposed algorithm/framework learns the statistical power manifold much faster as compared to a brute-force approach as the number of queries to the power oracle is significantly reduced. We also show that the quality of learning the manifold improves as the number of iterations increases for the genetic algorithm.