My student Filip Hermans defended his PhD thesis in May of this year. Thus far, I haven’t had time to blog or brag about it, but it is time I made up for that. I believe that what he has done is really worth taking a good look at, especially if you are interested in imprecise probabilities, the foundations of probabilistic inference, or stochastic processes.
There are, besides the Introduction and Conclusion, four main chapters in the thesis. The first deals with acceptability of gambles, and constitutes a valiant attempt at providing a foundation for (imprecise-)probabilistic inference based on weak and strict preference relations. It is the basis for a more recent and more detailed analysis that Erik Quaeghebeur, Filip and I have been working during over the last year (and which I will have occasion to talk about later). All other chapters are built on this framework. The second deals with (imprecise-)probabilistic inference associated with event trees, and provides the foundations for a theory of (discrete-time) stochastic processes using imprecise probabilities. In the third chapter, this is applied in particular to Markov processes. The fourth chapter extends the arguments of the previous two even further to allow for inference in credal networks with a tree structure.