Date: 2017-03-17

Time: 15:30-16:30

Location: BURN 1205

Abstract:

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures. We also relate Bayesian inference to the thermodynamic formalism in tracking dynamical systems.

Speaker

Sayan Mukherjee is a Professor in the Department of Statistical Science at Duke University. His research interest is in Geometry and topology in probabilistic modeling, Statistical and computational biology, Modeling of massive data.