On parameter estimation in population models II: multi-dimensional processes and transient dynamics

Recently, a computationally-efficient method was presented for calibrating a wide-class of Markov processes from discrete-sampled abundance data. The method was illustrated with respect to one-dimensional processes and required the assumption of stationarity. Here we demonstrate that the approach may be directly extended to multi-dimensional processes, and two analogous computationally-efficient methods for non-stationary processes are developed. These methods are illustrated with respect to disease and population models, including application to infectious count data from an outbreak of "Russian influenza" (A/USSR/1977 H1N1) in an educational institution. The methodology is also shown to provide an efficient, simple and yet rigorous approach to calibrating disease processes with gamma-distributed infectious period.