Penalized importance sampling for parameter estimation in stochastic differential equations

We consider the problem of estimating parameters of stochastic differential equations with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose a penalized importance sampling approach to approximate the transition density. Simulation studies in three different models illustrate promising improvements of the new penalized importance sampling 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.