Perturbed stochastic point processes as a novel tool for neural coding analysis

A latent internal process describes the state of some system, e.g. the membrane potential evaluation of a neuron, the social tension in a political conflict, the price of a stock, the strength of an industrial component or the health status of a person. When this process reaches a predefined threshold, the process terminates and an observable event occurs, e.g. a neuron releases an electrical impulse (also known as action potential or spike), the stock is sold/bought, the political conflict finishes, the industrial component breaks down or the person dies. Imagine an intervention, e.g., an input current, a speculation strategy, a political decision, maintenance of a component or a medical treatment, is initiated to the process before the event occurs. How can we evaluate whether the intervention had an effect? How can we detect the type of stimulus applied only observing the events following the intervention? What can be said if both the time of the intervention and the type of stimulus are unknown? Answering these questions is particularly difficult because the latent internal process describing the state of the system is perturbed, i.e. observed only on top of an indistinguishable background noise. From a mathematical point of view, the described problem can be modeled by stochastic point processes obtained as hitting times of perturbed stochastic processes. Our goal is to provide inference for the underlying process through series of hitting times, develop suitable statistical test and numerical algorithms and discuss them in the framework of information transfer in neural systems. Our background on inference for stochastic processes, stochastic numerics and neuroscience, and our expertise in combining theory, practice and simulations represents a perfect match for the project.