Title: Fast Iterated Filtering
Advisor: Associate Professor Edward Ionides
Committee Members: Associate Professor Yves Atchade, Assistant Professor Long Nguyen, Professor Mercedes Pascual, Professor Susan Murphy
Abstract: Partially observed Markov process (POMP) models are ubiquitous tools for modeling time series data in many sciences including statistics, econometrics, ecology and engineering. It can be difficult to make inference on these models due to the fact that measurements are incomplete, increasing the possibility of a weakly identifiable model. Standard methods for inference (e.g., maximum likelihood) with restrictive assumption of linear Gaussian model can lead to unsatisfactory results when the assumptions are violated. Fast iterated filtering methods, introduced in this proposal, can provide an asymptotically accurate and computationally efficient alternative. The key contribution is to demonstrate theoretically that by showing how the Fisher information can be approximated as a by-product of the inference methodology one can simultaneously achieve statistical consistency and computational efficiency without sacrificing the generalities of model assumptions. Another contribution is the extension of the methodology to be able to handle alternative data structures (e.g. panel data), flexible initial value parameter (IVP) set-tings (e.g. IVPs vector) and computational-efficient objective functions (e.g. pseudo-likelihood) in a feasible computing infrastructure (e.g. parallel computing). On validating the properties of the proposed methodology on a challenging inference problem of fitting a malaria transmission model with control to time series data, we find substantial gains for our methods over current alternatives.