LJKProbability & Statistics Seminar

On Thursday March 14 2013 at 14h00 in Salle 1  Tour IRMA

Seminary of Adeline SAMSON (Universite Paris Descartes / Laboratoire MAP5)

Estimation paramÃ©trique dans les modÃ¨les neuronaux

Summary

Parameter estimation in twodimensional 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 MorrisLecar model, where random ﬂuctuations in conductance and synaptic input are speciﬁcally accounted for by the diffusion terms.
It is deﬁned through a nonlinear twodimensional stochastic differential equation with only one coordinate observed. We aim at estimating the parameters of this stochastic MorrisLecar model. We propose a sequential Monte Carlo particle ﬁlter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudolikelihood through a stochastic version of the ExpectationMaximization algorithm. Performance on simulated data and real data are very encouraging.
