# Research

This page describes some of my research interests; for all the details you will have to take a look at my publications or presentations.

Way back, when I had to choose a topic for my MSc-thesis project, I already was very interested in Bayesian networks. Nowadays, Bayesian networks and related models are often called a probabilistic graphical model.

## Analysis and explanation of networks

The theory behind sensitivity analysis, mentioned below, can be used to study and explain properties of probabilistic models and conclude something about their general behaviour, or their robustness to inaccuracies in structure and parameters. In addition, concepts from e.g. QPNs (see below) allow for describing and explaining reasoning patterns in networks for real applications. In fact, a lot of research into topics related to constructing networks by hand can also be used in their explanation. Moreover, ideas from XAI can be tranfered to the domain of probabilistic graphical models; even interpretable models need explanation!

## Construction of networks

The research described below on QPNs and probability elicitation can be considered as research related to the
construction of the quantitative part of Bayesian networks. Instrumental to the fast quantification of Bayesian networks with expert-elicited probabilities is the availability of tools for *sensitivity analysis*.
Sensitivity analysis is a general technique for
studying the relationship between the input parameters and the output of a mathematical model. Sensitivity analysis
is a useful tool during quantification: you can use a fast and inaccurate method to elicit probabilities, and then use sensitivity analysis to investigate which parameters are strongly affecting your output, and spend more effort on getting those accurate. Sensitivity analysis can also be used to tune the parameters of your network, and study the effects of for example removing an arc from the network.

Other subjects of importance during network construction are properties of monotonicity that should be captured in the network, which may be induced or removed as a result of e.g. parameter tuning or discretisation.

## QPNs and verbal probability elicitation

For my MSc-thesis project I investigated *qualitative probabilistic networks (QPNs)* and proved some of their
properties. Qualitative probabilistic networks are basically abstractions of Bayesian networks, where the
conditional probability tables for the variables are replaced with signs of influences between variables.

For my PhD research I considered qualitative approaches to quantifying Bayesian networks. Since QPNs can be used as an intermediate step in the construction of Bayesian networks, we can benefit from the use of QPNs most if they are as powerful as possible. We therefore extended the basic framework in a number of ways; see for more details my summary of QPN research. In addition, I focused on methods for eliciting probabilities from domain experts. More specifically, we designed a verbal-numerical probability scale which enabled us to elicit the thousands of probabilities we required for a network on oesophageal cancer. Since our introduction of this elicitation tool, it has been used in the elicitation of probabilities for various real-life applications of Bayesian networks.