Large Deviation Asymptotics and Bayesian Posterior Consistency on Stochastic Processes and Dynamical Systems

Understand

We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency.

• Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss function, we specify the generalized posterior distribution.
• The problem of frequentist posterior consistency is concerned with whether as more and more samples are observed, the posterior distribution on parameters will asymptotically concentrate on the "right" parameters.
• We show that posterior consistency can be derived using a combination of classical large deviation techniques, such as Varadhan's lemma, conditional/quenched large deviations, annealed large deviations, and exponential approximations.