Title: Semi-complete data likelihood for efficient state space model fitting
Authors: Agnieszka Borowska - Vrije Universiteit Amsterdam (Netherlands) [presenting]
Ruth King - University of Edinburgh (United Kingdom)
Abstract: A novel efficient model-fitting algorithm for state space models is proposed. State space models are an intuitive and flexible class of models, frequently used due to the combination of their natural separation of the different mechanisms acting on the system of interest: the latent underlying system process; and the observation process. This flexibility, however, comes at the price of significantly more complicated fitting of such models to data as the associated likelihood is typically analytically intractable. For the general case a Bayesian data augmentation approach is often employed, 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. The proposed method circumvents the inefficiencies of the previous approaches by combining data augmentation with numerical integration in a Bayesian hybrid approach. This permits standard ``vanilla'' algorithms to be applied. The proposed semi-complete data augmentation algorithm is applied to different types of problems demonstrating efficiency gains in empirical studies.