A penalized simulated maximum likelihood approach in parameter estimation for stochastic differential equations

TL;DR

This paper introduces a penalized simulated maximum likelihood method for estimating parameters in stochastic differential equations with discrete, possibly sparse, and partially observed data, improving accuracy and efficiency.

Contribution

It develops a novel importance sampling approach with an auxiliary parameter embedded in a penalized likelihood framework for SDE parameter estimation.

Findings

Simulation studies show improved accuracy and efficiency.

Method effectively handles unobserved and sparsely observed states.

Applied successfully to real epidemic data.

Abstract

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown. We embed the auxiliary importance sampler in a penalized maximum likelihood framework which produces more accurate and computationally efficient parameter estimates. Simulation studies in three different models illustrate promising improvements of the new penalized simulated maximum likelihood method. The new procedure is designed for the challenging case when some state variables are unobserved and moreover, observed states are sparse over time, which commonly arises in ecological studies. We apply this new approach to two epidemics of chronic wasting disease in mule deer.