1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Operations Research, Department of Management Engineering, Technical University of Denmark3 Department of Management Engineering, Technical University of Denmark4 Technical Information Center of Denmark, Technical University of Denmark
During the last 10-15 years, the international community has become aware of the devastating mine contamination problems experienced in many post-conflict countries. As a consequence, a con siderable amount of money and time is spent on research and development in new ways of locating buried mines and unexploded ordnance in a fast and secure way. A major breakthrough is however still waiting, and a large fraction of the mine clearance, which still remains to be done, will therefore hinge on slow and dangerous procedures based on prodders and metal detectors. Realizing that landmine contamination is a phenomenon which cannot be eliminated overnight but is a problem which has to managed in several years to come, it is essential that the resources a national government in a mine affected country spends on mine clearance are used on the right projects. However, the identification of the mine clearance projects with the greatest impact is a delicate task. More systematic approaches to the ranking of minefields with respect to mine clearance can be found in the literature, but these methods are either founded on simple scoring rules or are of a more qualitative nature. Thus nobody seems yet to have examined the usefulness of the analytical tools which might be provided by operations research and statistics in order to support decision makers involved in national mine clearance programmes. In February 2002, the Danish Defence Research Establishment initiated in collaboration with the Technical University of Denmark a Ph.D.-project to investigate whether the application of operations research and statistics can support decision makers in Humanitarian Mine Action to make the prioritization of mine clearance operations more effective. The main part of that project, which is presented in the enclosed thesis, has concentrated on the development of a risk model quantifying to what extent a minefield poses a risk to a society. The risk model is derived in two steps: First, a general model, which requires detailed information about the mined area in question, is derived. Secondly, by the introduction of two additional assumptions, the general model is turned into a simple binomial model depending on two parameters m and q. In this context the integer m denotes the number of so-called functional mines in the minefield under consideration, and the parameter q denotes the probability of a randomly selected mine being encountered by a person, a vehicle, etc… during a predefined observation period. The true values of the binomial parameters, which jointly characterize the state of the mined area, will rarely be known in advance, but beliefs about these based on whatever information is available can conveniently be expressed in terms of probability distributions p(m) and p(q). This prepares the way for the introduction of Bayesian data analysis by which updates of the probability distributions can be generated from incoming accident statistics. The major obstacle to a real-life application of the derived risk model seems to be the lack of actual information about the binomial parameter q. A considerable part of the enclosed thesis focuses therefore on ways to provide information about q through statistical modelling. Depending on the level of historical information available to a hypothetical decision maker, two different proposed models are examined as ways of extracting information about q : 1) A simple hierarchical model which as input requires accident statistics and clearance reports from already cleared minefields; 2) A finite mixture model where only accident statistics and the specification of certain prior distributions are needed as input data. Common to both models is the generation of posterior distributions of the parameter q. To extract information about q from these distributions various simulation techniques are applied including importance sampling and Markov Chain simulation. The possibility of making updates of the entering probability distributions p(m) and p(q) through incoming accident statistics by the use of Bayes' rule makes the suggested risk model dynamic. Moreover, the application of Bayesian data analysis gives the derived risk model a very flexible structure which allows an accommodation to the varied circumstances found in Humanitarian Mine Action with respect to the amount of accessible information. The present thesis closes with an overall prescription for the synthesis of different pieces of information based on the concept of reference priors.