STA 290 Seminar Series
Tuesday, February 2, 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
**Joint BST 290 Seminar**
Speaker: Sayan Mukherjee (Duke University)
Title: “Inference and dynamics”
Abstract: I will talk about two problems that involve dynamics and inference.
The first problem is learning in dynamical systems. 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. 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.
The second problem is approximate Markov chain Monte Carlo (aMCMC). The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. We propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget.
Part I: Joint work with Kevin McGoff, Andrew Nobel, and Natesh Pillai
Part II: Joint work with James Johndrow, Jonathan Mattingly, and David Dunson