Marie Lilleborge

When comparing different ways of modeling discrete three-dimensional realizations such as facies, it is useful to have a measure of difference (or similarity) in the geometry of these realizations.We propose a method for evaluating such difference by comparing pattern counts for a small template. Tests on synthetic datasets demonstrate that the proposed difference effectively differentiates between realizations of a Boolean model and those generated using multiple-point statistics with the Boolean realizations as training images. We also observed that multiple-point statistics realizations based on similar training images yield smaller differences to one another compared to those based on training images from dissimilar concepts. This suggests that the proposed difference is a useful tool for comparing discrete three-dimensional realizations.

This study proposes a method to optimize the performance of BreastScreen Norway through a stratified recommendation of tests including independent double or single reading of the screening mammograms and additional imaging with or without core needle biopsy. This is carefully evaluated by a value of information analysis. An estimated graphical probabilistic model describing the relationship between a set of risk factors and the corresponding risk of breast cancer is used for this analysis, together with a Bayesian network modeling screening test results conditional on the true (but unknown) breast cancer status of a woman. This study contributes towards evaluating a possibility of improving the efficiency of the screening program, where all women aged 50 to 69 are invited every second year, regardless of individual risk factors. Our stratified recommendation of tests is dependent on the probability that an asymptomatic woman has developed breast cancer at the time she is invited to a screening.

We present upper and lower bounds for information measures, and use these to find the optimal design of experiments for Bayesian networks. The bounds are inspired by properties of the junction tree algorithm, which is commonly used for calculating conditional probabilities in graphical models like Bayesian networks. We demonstrate methods for iteratively improving the upper and lower bounds until they are sufficiently tight. We illustrate properties of the algorithm by tutorial examples in the case where we want to ensure optimality and for the case where the goal is an approximate solution with a guarantee. We further use the bounds to accelerate established algorithms for constructing useful designs. An example with petroleum fields in the North Sea is studied, where the design problem is related to exploration drilling campaigns. All of our examples consider binary random variables, but the theory can also be applied to other discrete or continuous distributions.

The optimal design of data acquisition is not obvious in Bayesian network models. The dependency structure may vary dramatically, which makes learning and information evaluation complicated and sometimes non-intuitive. The motivation for working on this topic is petroleum exploration, and the application of this paper is prospect selection in the North Sea. Here, the data gathering is often carried out during seasonal campaigns, and it is useful to plan the experimentation and to understand which data are likely to be most informative. Information measures are used to compare possible future observation sets. Four information measures are studied: Shannon Entropy, sum of variances, Node-wise Entropy and overall prediction error. The Shannon Entropy is commonly considered the standard measure of information, and the Node-wise Entropy measure can be interpreted as an approximation to the former. The variance measure links uncertainty and variance. The prediction error measure is tied to decision-making rules. The results lead to new insight about prospect selection. For example, the Node-wise Entropy and the variance measure behave similarly, and the optimal observation set of Shannon Entropy does not correspond to what one intuitively would consider as minimizing unknown information in this case.