We consider the problem of detecting an odd process among a group of Poisson point processes, all having the same rate except the odd process. The actual rates of the odd and non-odd processes are unknown to the decision maker. We consider a time-slotted sequential detection scenario where, at the beginning of each slot, the decision maker can choose which process to observe during that time slot. We are interested in policies that satisfy a given constraint on the probability of false detection. We propose a variation on a sequential policy based on the generalised likelihood ratio statistic. The policy, via suitable thresholding, can be made to satisfy the given constraint on the probability of false detection. Furthermore, we show that the proposed policy is asymptotically optimal in terms of the conditional expected stopping time among all policies that satisfy the constraint on the probability of false detection. The asymptotic is as the probability of false detection is driven to zero. We apply our results to a particular visual search experiment studied recently by neuroscientists. Our model suggests a neuronal dissimilarity index for the visual search task. The neuronal dissimilarity index, when applied to visual search data from the particular experiment, correlates strongly with the behavioural data. However, the new dissimilarity index performs worse than some previously proposed neuronal dissimilarity indices. We explain why this may be attributed to some experiment conditions.

Neuroscientists have recently shown that images that are difficult to find in visual search elicit similar patterns of firing across a population of recorded neurons. The$L^{1}$distance between firing rate vectors associated with two images was strongly correlated with the inverse of decision time in behavior. But why should decision times be correlated with$L^{1}$distance? What is the decision-theoretic basis? In our decision theoretic formulation, we model visual search as an active sequential hypothesis testing problem with switching costs. Our analysis suggests an appropriate neuronal dissimilarity index, which correlates equally strongly with the inverse of decision time as the$L^{1}$distance. We also consider a number of other possibilities, such as the relative entropy (Kullback–Leibler divergence) and the Chernoff entropy of the firing rate distributions. A more stringent test of equality of means, which would have provided a strong backing for our modeling, fails for our proposed as well as the other already discussed dissimilarity indices. However, test statistics from the equality of means test, when used to rank the indices in terms of their ability to explain the observed results, places our proposed dissimilarity index at the top followed by relative entropy, Chernoff entropy, and the$L^{1}$indices. Computations of the different indices require an estimate of the relative entropy between two Poisson point processes. An estimator is developed and is shown to have near unbiased performance for almost all operating regions.

We consider a visual search problem studied by Sripati and Olson where the objective is to identify an oddball 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 L1metric used by Sripati and Olson, this metric has the advantage of being firmly grounded in formal decision theory.