DNA microarray experiments provide a high throughput way to measure mRNA levels of thousands of genes simultaneously. This technology has been refined during the last 10 years and is now an important tool for molecular biologists. From a statistical point of view, the analysis of data generated with DNA microarrays is far from straightforward. The experiments involve several consecutive steps, each inducing systematic effects and differences in precision. Moreover, microarrays are both time consuming and expensive, so only few replicates are usually made. Thus, thousands of variables are observed only a few times each and there is a pressing need for quality assessments, which makes traditional statistical methods unsuitable. In this thesis a new method for analysis of paired DNA microarray experiments is presented. The method is based on a generalised linear model with a variance structure which consists of both a gene-independent covariance matrix and a gene-dependent scaling factor. To increase the precision, the latter is assumed to follow a prior distribution with a shape hyperparameter. These assumption makes the method suitable for handling data with quality variations and/or few replicates. Estimators for the covariance matrix as well as the hyperparameter are constructed and general likelihood ratio tests for differentially expressed genes are derived. Simulated datasets are used to show that the method

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