Active sequential hypothesis testing with application to a visual search problem

We consider a visual search problem studied by Sripati and Olson where the objective is to identify an odd ball image embedded among multiple distractor images as quickly as possible. We model this visual search task as an active sequential hypothesis testing problem (ASHT problem). Chernoff in 1959 proposed a policy in which the expected delay to decision is asymptotically optimal. The asymptotics is under vanishing error probabilities. We first prove a stronger property on the moments of the delay until a decision, under the same asymptotics. Applying the result to the visual search problem, we then propose a “neuronal metric” on the measured neuronal responses that captures the discriminability between images. From empirical study we obtain a remarkable correlation (r = 0.90) between the proposed neuronal metric and speed of discrimination between the images. Although this correlation is lower than with the L1 metric used by Sripati and Olson, this metric has the advantage of being firmly grounded in formal decision theory.