State-space models: the good, the bad and the ugly

Ruth King (University of Edinburgh, UK)

Latent process models are a very intuitive way of describing data observed over a series of time. They are frequently used due to the combination of their natural separation of the different mechanisms acting on the system of interest: the (unobserved) underlying system process; and the observation process. Considering each distinct process separately simplifies the model specification process, and provides a very flexible modelling approach. Fitting such models to data, however, can be significantly more complicated, as the associated likelihood is typically analytically intractable. For the general case a Bayesian data augmentation approach is often used, where the true unknown states are treated as auxiliary variables and imputed within the MCMC algorithm. However, standard "vanilla" MCMC algorithms may perform very poorly due to high correlation between the imputed states, leading to the need to specialist algorithms being developed. In this talk I will propose a novel efficient model-fitting algorithm combining the ideas of data augmentation and numerical integration permitting standard "vanilla" algorithms to be applied. Two examples relating to stochastic volatility and population count data will be considered to demonstrate the increased efficiency that can be obtained using the new algorithm.