Analysis of Spatial Patterns in Tissue Samples using Spectral Analysis and GMRF Modelling

First, we would like to express our gratitude towards our supervisor, Maria Sandsten, whos help and support has been invaluable to us. We would like to thank Johan Lindstrom for his help regarding the theory of Gaussian Markov random elds. We would also like to thank Jonas Erjefalt and Caroline Sanden at Medetect AB, as well as Jimmie Jonsson at Medetect AB for all the help with the tissue data. Biotechnology company Medetect AB has developed a technology for staining of multiple cell types in the same tissue sample enabling positioning of cells as well as giving a way to distinguish between cell types. With new methods of visualising human tissue at a cellular level, comes a need to analyse this data. In this thesis, we therefore investigate some new methods, spectral non-parametric as well as spatial and parametric, of analysing the structure of possibly mul-tivariate point sets. Both spatial structure of univariate point data as well a