Parameter estimation of a two-dimensional stochastic differential equation partially observed with application to neuronal data analysis

Statistics and Modeling for Complex Data
SAMSON Adeline

Stochastic differential systems have been widely developed to describe neuronal activity by taking into account the random behavior of neurons. We focus on the stochastic two-dimensional Morris Lecar model, which drift and volatility functions are non-linear functions of the process and depend on unknown physiological parameters. Statistical estimation of these parameters from neuronal data is very difficult. Indeed, neuronal measurements correspond to discrete observations of only the first coordinate of the system. Furthermore, the SDE has no explicit solution. We propose an estimation method based on a stochastic version of the EM algorithm, the SAEM algorithm, which requires the simulation of the hidden coordinate conditionally to the observations. We propose to perform this simulation step with a particle filter based on the Euler approximation of the SDE. We prove the almost sure convergence of the obtained estimator towards the maximum of the 'exact' likelihood, without Euler approximation. We illustrate the performance of our estimation method on simulated and real data. This is a joint work with Susanne Ditlevsen (Copenhagen).