Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions

We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended backward induction to arbitrary choice functions, yielding far more efficient solutions, and we identified simple necessary and sufficient conditions for this to work. In this paper, we show that backward induction works for maximality and E-admissibility, but not for interval dominance and Gamma-maximin. We also show that, in some situations, a computationally cheap approximation of a choice function can be used, even if the approximation violates the conditions for backward induction; for instance, interval dominance with backward induction will yield at least all maximal normal form solutions

A sensitivity analysis and error bounds for the adaptive lasso.

Sparse regression is an efficient statistical modelling technique which is of major relevance for high dimensional problems. There are several ways of achieving sparse regression, the well-known lasso being one of them. However, lasso variable selection may not be consistent in selecting the true sparse model. Zou (2006) proposed an adaptive form of the lasso which overcomes this issue, and showed that data driven weights on the penalty term will result in a consistent variable selection procedure. Weights can be informed by a prior execution of least squares or ridge regression. Using a power parameter on the weights, we carry out a sensitivity analysis for this parameter, and derive novel error bounds for the Adaptive lasso

Model checking for imprecise Markov chains.

We extend probabilistic computational tree logic for expressing properties of Markov chains to imprecise Markov chains, and provide an efficient algorithm for model checking of imprecise Markov chains. Thereby, we provide a formal framework to answer a very wide range of questions about imprecise Markov chains, in a systematic and computationally efficient way

Robust decision analysis under severe uncertainty and ambiguous tradeoffs: an invasive species case study

Bayesian decision analysis is a useful method for risk management decisions, but is limited in its ability to consider severe uncertainty in knowledge, and value ambiguity in management objectives. We study the use of robust Bayesian decision analysis to handle problems where one or both of these issues arise. The robust Bayesian approach models severe uncertainty through bounds on probability distributions, and value ambiguity through bounds on utility functions. To incorporate data, standard Bayesian updating is applied on the entire set of distributions. To elicit our expert's utility representing the value of different management objectives, we use a modified version of the swing weighting procedure that can cope with severe value ambiguity. We demonstrate these methods on an environmental management problem to eradicate an alien invasive marmorkrebs recently discovered in Sweden, which needed a rapid response despite substantial knowledge gaps if the species was still present (i.e., severe uncertainty) and the need for difficult tradeoffs and competing interests (i.e., value ambiguity). We identify that the decision alternatives to drain the system and remove individuals in combination with dredging and sieving with or without a degradable biocide, or increasing pH, are consistently bad under the entire range of probability and utility bounds. This case study shows how robust Bayesian decision analysis provides a transparent methodology for integrating information in risk management problems where little data are available and/or where the tradeoffs are ambiguous