Research interests

My research is concerned with the theoretical study of imprecise probability models, and with the design of efficient computational methods that allow these models to be used for statistical inference and decision making.

Simply put, imprecise probability models are just sets of probability models: whenever it is infeasible to reliably estimate a single probability, a set of probabilities is used instead, each of whose elements is regarded as a candidate for some ideal true probability. In this sense, imprecise probability theory is an extension of probability theory that combines probabilistic uncertainty and model uncertainty into a single theory. However, this simplified view is only one of the many ways to look at or interpret imprecise probabilities. Among the many other imprecise-probabilistic frameworks that exist, I favour lower previsions and sets of desirable gambles.

From an applied point of view, imprecise probability models are useful whenever sharp, precise and trustworthy assessments of probabilities are not available, for example because it is too difficult, costly, or time-consuming to gather sufficient data or expert knowledge. In such cases, standard probability models, and the inferences and decisions that are obtained by them, are often unreliable. Imprecise probability models avoid this problem by allowing for partial probability assessments such as bounds on probabilities. The resulting inferences and decisions are robust with respect to variations within these bounds, and will therefore remain reliable even in cases of severe uncertainty.

Credal networks

Within the field of imprecise probabilities, my main research topic is credal networks, which are probabilistic graphical models that generalise Pearl's celebrated Bayesian networks to the framework of imprecise probabilities, including special cases such as hidden Markov models and Markov chains. Basically, the main difference is that the local uncertainty models of a credal network are allowed to be imprecise, whereas a Bayesian network only considers probability distributions. This extra feature allows for more flexible modelling, and results in inferences and decisions that are more reliable. However, it also comes at a price: computing inferences in credal networks tends to be very complex, and efficient algorithms typically apply to specific inference problems only. Much of my research aims at reducing this complexity, by developing efficient algorithms for new types of inference problems.

In the context of my PhD, I have focussed on one particular type of credal networks, called credal networks under epistemic irrelevance. I have studied their theoretical properties, and have used these properties to design algorithms for them that can efficiently solve large classes of inference problems. Interestingly, these classes include problems that are known to be NP-hard for other types of credal networks, such as credal networks under strong or complete independence. More recently, I have also designed some algorithms for these other types of credal networks, but only for specific inference problems.

My next goal is to develop a new type of credal networks, called mixed credal networks, that combines the best features of existing types of credal networks, and to design inference algorithms for these mixed credal networks that are as efficient as their Bayesian network counterparts.

Stochastic processes

I am also interested in stochastic processes, and in particular, in their extension to the framework of imprecise probabilities. Initially, because of their link with credal networks, I focussed on imprecise versions of discrete-time Markov chains. By now, my interest has broadened to include imprecise Poisson processes, imprecise Dirichlet processes, imprecise multinomial processes and imprecise continuous-time Markov chains. My research on these processes ranges from foundational topics such as exchangeability and limit theorems, over computational aspects such as the development of optimisation techniques, up to applications to statistical inference and queueing theory.

My most recent as well as current work on stochastic processes is devoted to the theoretical study of imprecise continuous-time Markov chains, and to the development of efficient optimisation techniques for them.

Other topics

Besides on credal networks and stochastic processes, I have also worked on, and remain interested in, a number of other topics, all within the realm of imprecise probabilities. The following list provides a brief overview:

  • Imprecise extensions of the Viterbi algorithm
  • Credal classifiers and their empirical evaluation
  • Martingale-theoretic approaches to imprecision: foundations, ergodic theorems, ...
  • Imprecise extensions of optimal control algorithms
  • Conditioning on events with (lower) probability zero
  • Extreme lower previsions
  • Sensitivity analysis

“La théorie des probabilités n’est, au fond, que le bon sens réduit au calcul;
elle fait apprécier avec exactitude ce que les esprits justes sentent par une sorte d'instinct,
sans qu'ils puissent souvent s'en rendre compte.”

– Pierre-Simon Laplace