We will start by presenting the general framework of Bayesian hierarchical dynamic models (BHDM) for space-time data. Within this framework, we will consider in some detail the special case of linear dynamics. We will review MCMC estimation for conditionally linear dynamic models. We will introduce integro-differential models and give a SPDE justification that provides insights into the connections between the dynamics of the process and the properties of the kernel defining the IDE. Using a spectral representation we will formulate the IDE estimation problem as a BHDM and then explore flexible non parametric representations of the kernel in order to better approximate non-linear dynamics with a conditional linear structure.
Bruno Sansó is Professor, Department Statistics, University of California Santa Cruz. Sansó's PhD is from Universidad Central de Venezuela, 1992. He is an expert in Bayesian hierarchical models for spatio-temporal models, extreme values, computer model emulation and calibration, and point processes. His work focuses on environmental and climatological applications. Sansó was Professor and co-founder of the Department of Scientific Computing and Statistics, Universidad Simón Bolívar, Venezuela. In 2001 he joined the University of California Santa Cruz Department of Applied Mathematics and Statics, being department chair during 2009-2014. He has supervised many graduate students. One of them won the Savage Award in 2010. Sansó's publications have appeared in the most highly ranked statistical journals, obtaining some prestigious awards, like the Mitchell Prize in 2009 and 2019. Sansó was Associate Editor of JSPI and Technometrics. He was Editor in Chief of the journal Bayesian Analysis. He has had appointed and elected leadership roles in the American Statistical Association, the International Environmetrics Society, The Bernoulli Society and the International Society for Bayesian Analysis. Sansó is Elected Member of the International Statistical Institute, Fellow of the American Statistical Association, and Fellow of the International Society for Bayesian Analysis.