On Bayesian Asymptotics in Stochastic Differential Equations with Random Effects

TL;DR

This paper explores Bayesian methods for estimating population parameters in stochastic differential equations with random effects, establishing consistency and asymptotic normality of the posterior distribution in both iid and non-iid settings.

Contribution

It extends previous work by analyzing Bayesian asymptotics for SDEs with random effects, including non-iid cases, and proves key properties of the posterior distribution.

Findings

Posterior distribution is consistent in iid and non-iid cases.

Asymptotic normality of the posterior is established.

Bayesian approach complements existing frequentist results.

Abstract

Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs are independent and identical (iid). In this article, we consider the Bayesian approach to learning about the population parameters, and prove consistency and asymptotic normality of the corresponding posterior distribution in the iid set-up as well as when the SDEs are independent but non-identical.