Mr. Jarad Niemi (Duke University)

Title: Computational approaches for general state-space models

Abstract: State-space models are widely used for analysis of time series data in fields such as biology, finance, epidemiology, and others. In a Bayesian context, simultaneous state and fixed parameter estimation are performed using either Markov chain Monte Carlo if the data are collected in batch or Sequential Monte Carlo when the data are analyzed in real-time. I will discuss developments in these fields that exploit the use of mixtures of distributions. In the MCMC context, filtering and smoothing is accomplished using mixtures that provide Metropolis proposals for the entire latent state series. In the SMC context, approximating filtered distributions for fixed parameters provides a means to regenerate parameter draws and combining this with sufficient statistic methods enriches the class for which those methods can be used. We draw on motivating examples from biology and finance to illustrate the methodologies.