Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging

摘要

Hypothesis testing is a classical methodology of making decisions using experimental data. In hypothesis testing one seeks to discover evidence that either accepts or rejects a given null hypothesis H_0. The alternative hypothesis H_1 is the hypothesis that is accepted when H_0 is rejected. In hypothesis testing, the probability of deciding H_1 when in fact H_0 is true is known as the false alarm rate, whereas the probability of deciding H_1 when in fact H_1 is true is known as the detection rate (or power) of the test. It is not possible to optimize both rates simultaneously. In this paper, we consider the problem of determining the data to be used for hypothesis testing that maximize the detection rate for a given false alarm rate. We consider in particular a hypothesis test which is relevant in functional magnetic resonance imaging (fMRI).