Monte Carlo Likelihood Estimation of Mixed-Effects State Space Models with Application to HIV Dynamics

The statistical inference for generalized mixed-effects state space models (MESSM) are investigated when the random effects are unknown. Two filtering algorithms are designed both of which are based on mixture Kalman filter. These algorithms are particularly useful when the longitudinal measurements are sparse. The authors also propose a globally convergent algorithm for parameter estimation of MESSM which can be used to locate the initial value of parameters for local while more efficient algorithms. Simulation examples are carried out which validate the efficacy of the proposed approaches. A data set from the clinical trial is investigated and a smaller mean square error is achieved compared to the existing results in literatures.