Statistical inference for perturbed stochastic processes with applications to neuroscience

The formal representation of series of uniform events appearing randomly in time as a stochastic point process is common in several branches of applications, such as biology, finance, medicine, neuroscience, physics, psychology and reliability theory. In this project we consider stochastic point processes obtained as hitting times of perturbed stochastic processes, either diffusion or jump processes, and discuss them in the framework of information transfer in neural systems. Our aim is to provide inference for the underlying process through the series of passage times, as well as developing suitable statistical test and numerical algorithms. This is particularly difficult because the series of events is observed on top of an indistinguishable background signal. 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.