Dr. Jarad Niemi (UCSB)

Title: A sequential Monte Carlo primer

Abstract: State-space models are widely used for time series analysis. Typically data arrive sequentially in time and therefore inferential techniques that utilize this structure are preferred. When only the latent states are unknown, sequential importance sampling is a natural candidate, but suffers from severe particle attrition. Sequential importance sampling with resampling, otherwise known as the bootstrap filter, dramatically reduces this attrition by propagating only those particles with meaningful importance weights. The auxiliary particle filter further improves performance by forecasting which particles will have meaningful importance weights. Neither of these methods are suitable for simultaneous latent state and fixed parameter inference due to degeneracy in fixed parameter estimation. A flexible approach to simultaneous inference approximates the particulate distribution using a kernel density based on a mixture of multivariate normals. A better approach from a particle degeneracy perspective uses sufficient statistics to carry parameter inferences. When combined with a resample-propagate step, this approach is termed particle learning. We conclude this talk by discussing outstanding statistical questions in the sequential Monte Carlo literature.