Computational methodologies for state-space models: A Big-Data challenge

The ready availability of data requires improved methods for model fitting. Within this project, we will explore Bayesian approaches to handle the large class of state-space models, with a particular focus on model design, to capture the information contained in large amounts of data. High dimensionality and large sample sizes pose serious challenges in model selection and inference. In fact, model components such as the likelihood itself and the state transformation density, are usually intractable under the above conditions and regular approaches based on Bayes factors, for example, cannot be implemented. In this project, new approaches to deal with Big-Data problems within the Bayesian context will be explored and developed with the aim of overcoming modelling and current computational limitations. Besides methodological investigations, supported by simulated data, the project will also involve practical applications, in particular to the areas of finance and ecology.