Mixedsde: A package to fit mixed stochastic differential equations

Abstract

Stochastic differential equations (SDEs) are useful to model continuous stochastic processes. When (independent) repeated temporal data are available, variability between the trajectories can be modeled by introducing random effects in the drift of the SDEs. These models are useful to analyze neuronal data, crack length data, pharmacokinetics, financial data, to cite some applications among other. The R package focuses on the estimation of SDEs with linear random effects in the drift. The goal is to estimate the common density of the random effects from repeated discrete observations of the SDE. The package mixedsde proposes three estimation methods: a Bayesian parametric, a frequentist parametric and a frequentist nonparametric method. The three procedures are described as well as the main functions of the package. Illustrations are presented on simulated and real data.