UE Stochastic modelling for neurosciences

Diplômes intégrant cet élément pédagogique :

Descriptif

Biophysical processes observed in neurosciences are very complex. The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail. This course gives an introduction to the field of theoretical and computational neuroscience with a focus on models of single neurons. Neurons encode information about stimuli in a sequence of short electrical pulses (spikes).

Topic 1: The first part will  present the main stochastic neuronal models: integrate-and-fire neural models, Hodgkin-Huxley models and biophysical modeling

Topic 2: The second part will give present the mathematical tools required to fit neuronal models to neuronal data: stochastic calculus, stochastic differential equations, maximum likelihood

Topic 3: The last part will introduce the case of partial observations of complex neuronal models. These statistical methods are based on EM algorithm, Markov chain Monte Carlo, sequential Monte Carlo and particle filtering, model selection.

Pré-requis

Probability, estimation, maximum likelihood

Compétences visées

At the end of the course, the student will be able to implement a MCMC or a particle filter to estimate parameters of stochastic models

Informations complémentaires

Méthode d'enseignement : En présence
Lieu(x) : Grenoble - Domaine universitaire
Langue(s) : Anglais