A Particle Filter Approach to Multiprocess Dynamic Models with Application to Hormone Data

Abstract

We extend the multiprocess dynamic models to the general non-Gaussian and nonlinear setting. Under this framework, we propose specific models to simultaneously model hormone smooth basal trend and pulsatile activities. The pulse input is modeled by two processes: one as a point mass at zero and one as a gamma distributed random variable. This gamma-driven approach ensures the pulse estimates to be nonnegative, which is an intrinsic characteristic of hormone dynamics. The smooth trend is modeled by smoothing splines. Both additive and multiplicative observational errors are investigated. Parameters are estimated by maximizing the marginal likelihood. Baseline and pulses are estimated by posterior means. For implementation, particle filter is adopted. Unlike the traditional condensation method where a single distribution is used to approximate a mixture of distributions, this particle filter approach allows the model components to be accurately evaluated at the expense of computational resources. The specific models are applied to a cortisol series. The finite sample performance is evaluated by a simulation. The data application and the simulation show that the biological characteristics can be incorporated and be accurately estimated under the proposed framework.