I would like to thank Petros Dellaportas'. This is the first phrase that comes to mind. I would like to thank him for changing my way of thinking and living. He helped me understand that only through hard work in chorus with an open mind, can one strive forward. He taught me to leave nothing to chance and to intuititively explore and thoroughly investigate every small detail in depth. Moreover he introduced me to the world of Bayesian statistics, that has presented me with the challenges I have always anticipated, thus becoming my preferred field of research. It would require more than just the pages of this Thesis to describe my feelings for Petros, hence I must stop here and solely express my gratitude and the great honor it was for me to be his PhD student.The second person I would like to thank is Ioannis Ntzoufras, for the rather analytical and extensive conversations we had on several aspects of my research. Ioannis also gave me the chance to be a tutor for the courses Data analysis and Biostatistics during my PhD. Moreover Ioannis was always an open person with constant willingness to help and offer knowledge, while I must also say I admire him for his work in the field of Bayesian statistics.A rather special person I would like to thank is Elias Tzavalis. During my PhD he offered me the chance to write with him a book on investments, an experience through which I acquired significant knowledge on several aspects of finance. Furthermore, Elias gave me the chance to a be a tutor for the courses investments appraisal and portfolio management. Our cooperation during all these years was rather productive and enlightening for me.I feel lucky I have had the opportunity to study in the department of Statistics of the Athens University of Economics and Business, where I met and collaborated with many interesting people. Bright examples, among many, are Ioannis Vrontos and Dimitris Karlis who were both an admirable source of inspiration for me. I would like to especially thank Ioannis Vrontos for the very instructive comments during the revision process of the Thesis. Furthermore, I must refer to Tasos Plataniotis, who as a co-student in the PhD programme, was always encouraging me to go on, while we spent endless hours discussing each others problems. The environment in the department was always friendly and research stimulating, while I was given the chance to attend a series of meetings and conferences.Finally I would like to thank the Propondis Foundation for the financial support during my PhD years, as well as the director of the Foundation, Ioannis Baveas for his ethical support.