Pierre Jacob

Estimation of the derivatives of the log-likelihood in latent variable models

Ionides, King et al. (Inference for nonlinear dynamical systems, PNAS 103) have introduced an original approach to perform maximum likelihood parameter estimation in state-space models which only requires being able to simulate the latent Markov model according its prior distribution. Their methodology bypasses the calculation of any derivative by expressing the score in the original model as an expectation under a modified model. Building upon this insightful work, we provide here similar "derivative-free" estimators for the score and the observed information matrix. We discuss the properties of the estimator and compare them with finite difference estimators.