Estimation paramétrique dans les modèles neuronaux

Parameter estimation in two-dimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem.
The membrane potential evolution in single neurons can be measured at high frequency, but biophysical realistic models have to include the unobserved dynamics of ion channels. One such model is the stochastic Morris-Lecar model, where random fluctuations in conductance and synaptic input are specifically accounted for by the diffusion terms.
It is defined through a non-linear two-dimensional stochastic differential equation with only one coordinate observed. We aim at estimating the parameters of this stochastic Morris-Lecar model. We propose a sequential Monte Carlo particle filter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudo-likelihood through a stochastic version of the Expectation-Maximization algorithm. Performance on simulated data and real data are very encouraging.