Quickest detection of state-transition in point processes: Application to neuronal activity

Quickest detection is the problem of detecting a change in the probability distribution of a sequence of random observations with as little delay as possible and with low probability of false alarm. To date, algorithms for quickest detection exist mainly for cases where the random observations are independent, and linear or exponential cost functions of the delay are used. We propose a dynamic programming algorithm to solve the quickest detection problem when dependencies exist among the observations, and for any nondecreasing cost function of the detection delay. We implement the algorithm for a Bayesian formulation (i.e., the change time T in the probability distribution of the observations is a random variable with a geometric distribution) when the observations distribute according to two distinct point processes. We apply the algorithm to spiking activity observations from neurons recorded in the subthalamic nucleus of Parkinson´s disease patients during the execution of a motor task. The algorithm exploits the point-process characterization of the spike trains before and during movement (two states), and optimally detects the state transition at movement onset. Performances significantly (i.e., with a p-value p<;0.05) increase over a chance level predictor and Bayesian estimator.