This thesis is concerned with parameter estimation for multivariate diffusion models. It gives a short introduction to diffusion models, and related mathematical concepts. we then introduce the method of prediction-based estimating functions and describe in detail the application for a two-dimensional Ornstein-Uhlenbeck where one coordinate is completely unobserved. This model does not have the Markov property and it makes parameter inference more complicated. Next we take a Bayesian approach and introduce some basic Markov chain Monte Carlo methods. In chapter ve and six we describe an Bayesian method to perform parameter inference in multivariate diffusion models that may be only partially observed. The methodology is applied to the stochastic FitzHugh-Nagumo model and the two-dimensional Ornstein-Uhlenbeck process. Chapter seven focus on parameter identifiability in the aprtially observed Ornstein-Uhlenbeck process, while chapter eight describes the detials of an R-package that was developed in relations to the application of
the estimationprocedure of chapters five and six.