Abstract

Markov population processes are popular models for studying a wide range of phenomena including the spread of disease, the evolution of chemical reactions and the movements of organisms in population networks (metapopulations). Our ability to use these models can effectively be limited by our knowledge about parameters, such as disease transmission and recovery rates in an epidemic. Recently, there has been interest in devising optimal experimental designs for stochastic models, so that practitioners can collect data in a manner that maximises the precision of maximum likelihood estimates of the parameters for these models. I will discuss some recent work on optimal design for a variety of population models, beginning with some simple one-parameter models where the optimal design can be obtained analytically and moving on to more complicated multi-parameter models in epidemiology that involve latent states and non-exponentially distributed infectious periods. For these more complex models, the optimal design must be arrived at using computational methods and we rely on a Gaussian diffusion approximation to obtain analytical expressions for the Fisher information matrix, which is at the heart of most optimality criteria in experimental design. I will outline a simple cross-entropy algorithm that can be used for obtaining optimal designs for these models. We will also explore some recent work on optimal designs for population networks with the aim of estimating migration parameters, with application to avian metapopulations.