Statistical inference for partially observed diffusion processes

The thesis is concerned with parameter estimation for discretely observed multivariate diffusion models where some coordinates may be completely unobserved. Special attention is given to the two-dimensional Ornstein-Uhlenbeck (OU) model and the stochastic Fitz-Hugh-Nagumo (FHN) model.

 The method of prediction-based estimating functions is introduced and applied to the two-dimensional OU-process where one coordinate is completely unobserved. This model does not have the Markov property and it makes parameter inference complicated. Furthermore, for partially observed diffusions, parameter identifiability is an important issue, and this is considered in some detail for the partially observed OU model. 

 We then introduce some basic Markov Chain Monte Carlo methods and describe a Bayesian method to perform parameter inference in multivariate diffusion models that may be only partially observed. These methods are highly computer intensive and they are not implemented in standard software. Thus an R package (BIPOD) was developed in order to implement the Bayesian estimation procedures. 

 The Bayesian methodology is applied to the stochastic FHN-model and the two-dimensional OU-model for both the partially and the fully observed case.

 Principal supervisor: Susanne Ditlevsen

 Assessment committee: 

Chairman, Prof. Niels Richard Hansen, Department of Mathematical Sciences

 Prof. Adeline Sampson, l'Université Joseph Fourier, Grenoble

 Prof. Erik Lindström, Lund University