Claus Dethlefsen, Aalborg University

Space-time problems and applications
	
ABSTRACT:
	
 State space models and Kalman filter techniques have been widely used
 for the analysis of time series. Typically, a latent process is
 assessed from observations using filtering (the present), smoothing
 (the past) and/or prediction (the future). The model class is very
 broad and comprises ARIMA models, cubic spline models and structural
 time series models. The development of state space theory has
 interacted with the development of other statistical disciplines.
 
 In particular, we consider Markov random field models. These are
 spatial models applicable in e.g. disease mapping and in agricultural
 experiments. Recently, the Gaussian Markov random field models were
 expressed as state space models, enabling the Kalman filter
 machinery. Our main contribution is to extend the Markov random field
 models by generalising the corresponding state space model. It turns
 out that several non-Gaussian spatial models can be analysed by
 combining approximate Kalman filter techniques with importance
 sampling.
 
 Reference: C. Dethlefsen. Markov random field extensions using state
 space models. In J.M. Bernardo, M.J. Bayarri, J.O. Berger,
 A.P. Dawid, D. Heckerman, A.F.M.  Smith, and M. West, editors,
 Bayesian Statistics 7. Oxford University Press, 2003.