Statistical Approaches for Probabilistic Model Checking

In this dissertation, we survey the different techniques used to perform statistical probabilistic model checking, prove their respective validity and compare them in terms of (statistical) reliability. We then propose some extensions of these methods for computation of rewards, which to our knowledge has not been done before. All these strategies are added to the code of the probabilistic model checking tool PRISM, and we experiment them on several large biological model examples. We conclude by some recommendations for the practical use of these methods, based on the experiments observation and the methods comparisons. 1 Acknowledgements I would like to thank Dr David Parker for the supervision of this thesis. He proposed me an interesting and challenging subject, introduced the PRISM code to me, proofread this dissertation and was always present to advise me in the direction to give to my researches. During this project, I studied a part of the method that APMC implements, and I really appreciated the explanations of Dr Sylvain Peyronnet about this and the choices he and his team made when they wrote this software. I am grateful to Mr Bernard Sufrin for the supervision of my Master in general and for his advice and discussions all along the year. I would also like to thank my French engineering school, the École Nationale Supérieure pour l'Industrie et l'Entreprise (ENSIIE), for offering me the opportunity to follow this Master of Science in the University of Oxford. Finally, many thanks to my family, my friends and all the people in the Computing Laboratory for their smiles, their kindness and their support.