In this thesis the maximum a posteriori (MAP) approach to synthetic aperture radar (SAR) analysis is reviewed. The MAP model consists of two probability density functions (PDFs): the likelihood function and the prior model. Contributions related to both models are made. As the first contribution a new likelihood function describing the multilook three-polarisation intensity SAR speckle process, which is equivalent to the averaged squared amplitude samples from a three-dimensional complex zero-mean circular Gaussian density, has been derived. This PDF is a correlated three-dimensional chi-square density in the form of an infinite series of modified Bessel functions with seven independent parameters. Details concerning the PDF such as the estimation of the PDF parameters from sample data and the moments of the PDF are described. The new likelihood function is tested against simulated and measured SAR data. The second contribution is a novel parameter estimation method for discrete Gibbs random field (GRF) prior models. Given a quantity of sample data, the parameters of the GRF model, which comprise the values of the potential functions of individual cliques, are estimated. The method uses an error function describing the difference between the local model PDF and the equivalent estimated from sample data. The concept of "equivalencies" is introduced to simplify the process. The new parameter estimation method is validated and compared to Besag's parameter estimation method (coding method) using GRF realisations and other sample data.