Markov Controlled Excursions, Local Alignment and Structure

From Markov additive processes to biological sequence analysis ii Preface This thesis constitutes my Ph.D.-thesis – a part of the requirements for achieving the Ph.D. degree at the The subject of the thesis is probability and bioinformatics – as viewed from a person inclined to do mathematical research. As it turned out, the thesis is highly mathematical and the scientific contribution of the thesis is mostly to the theory of probability and mathematical statistics. Theories and results about the tools used in bioinformatics – in particular biological sequence analysis – are developed, and hopefully this will result in improved tools for other bioinformaticians to benefit from. The subject of bioinformatics and biological sequence analysis was kindly suggested by my supervisors, Professor Michael Sørensen and Associate Professor Ernst Hansen, whom I owe a lot for their qualified guidance throughout this project. They have made up a good team. Ernst and Michael have also played a key role in establishing good and useful connections to biologist and bioinformaticians. I will mention Professor Peter Arctander and his group at the They have provided me with much inspiration for the practical applications of the work presented in this thesis. In this connection I want to thank Morten Lindow at the Bioinformatics Centre, who extracted the RNA-data presented in Chapter 7 in a useful format. I would also like for hosting me when visiting Chalmers and Stanford respectively. In particular, I would like to thank David Siegmund for useful iii iv Preface suggestions in relation to an early version of Chapter 5 and Chapter 6 and for many inspiring discussions about statistics and probability theory in biological sequence analysis. Furthermore, I would like to thank everybody at the Department of Applied Mathematics and Statistics for all having contributed to this thesis in one way or the other. I want to mention Martin Jacobsen with whom I have had some valuable discussions, and, most notably, I want to thank Anders Tolver Jensen for not just being a good colleague and a close collaborator, with whom I have discussed my work for many hours, but also for being a very good friend. Our collaboration was fruitful and the results presented in Chapter 3 of this thesis are jointly produced. I also want to thank Anders Tolver Jensen for help with proofreading part of this manuscript. Last but not least I want to thank my small but enlarging …