Department of Statistics, Duke University
Title: Consistency of maximum likelihood estimation for some dynamical systems
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. Our proof involves ideas from both information theory and dynamical systems. 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.
Sayan Mukherjee is an Associate Professor in Statistical Science, Mathematics, and Computer Science and an investigator in the Institute for Genome Sciences & Policy at Duke University. He completed a PhD from MIT in the Center for Biological and Computational Learning and was a Postdoctoral Fellow at the Broad Institute of MIT and Harvard. His research areas include topology and geometry in statistical inference, inference in dynamical systems, large scale machine learning algorithms, computational biology, and Bayesian statistics.