Abstract:
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Parameter estimation in multi-dimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, 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. Furthermore, noise may be introduced only on some of the coordinates. We consider neuronal multi-dimensional stochastic models with coupled coordinates (the non observed coordinates are non-autonomous) in the elliptic or hypoelliptic cases. Therefore the hidden Markov model framework is degenerate, and available methods break down. This talk will present statistic methods in this ill-posed situation: parametric methods with particle filter approach or contrast estimator of drift and diffusion coefficient parameters; non-parametric methods with kernel estimators of the drift and diffusion coefficient.
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