Parameter Estimation for Partially Observed Time-Changed SDEs

TL;DR

This paper introduces new MCMC algorithms for parameter estimation in partially observed time-changed SDEs, enabling likelihood and Bayesian inference with proven efficiency and tested on real and simulated data.

Contribution

It develops unbiased score-based stochastic approximation and multilevel Bayesian methods for efficient parameter estimation in complex stochastic models.

Findings

Achieves mean square error of O(ε^2) with cost O(ε^{-2} log(ε)^2)

Develops new MCMC algorithms for likelihood and Bayesian estimation

Validated methods on simulated and real data

Abstract

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop new Markov chain Monte Carlo (MCMC) algorithms which allow an unbiased score-based stochastic approximation method to provide likelihood-type parameter estimators. We also use a variant of this MCMC algorithm to perform multilevel-based Bayesian parameter estimation. We prove that this latter method achieves a mean square error of $\mathcal{O}(\epsilon^2)$ ($\epsilon>0$) with a cost of $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$. Our methodologies are tested numerically on both simulated and real data.