18,143 research outputs found
Decision-Making with Belief Functions: a Review
Approaches to decision-making under uncertainty in the belief function
framework are reviewed. Most methods are shown to blend criteria for decision
under ignorance with the maximum expected utility principle of Bayesian
decision theory. A distinction is made between methods that construct a
complete preference relation among acts, and those that allow incomparability
of some acts due to lack of information. Methods developed in the imprecise
probability framework are applicable in the Dempster-Shafer context and are
also reviewed. Shafer's constructive decision theory, which substitutes the
notion of goal for that of utility, is described and contrasted with other
approaches. The paper ends by pointing out the need to carry out deeper
investigation of fundamental issues related to decision-making with belief
functions and to assess the descriptive, normative and prescriptive values of
the different approaches
Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence
Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling
Optimisation under uncertainty applied to a bridge collision problem
We consider the problem of modelling the load on a bridge pillar when hit by a vehicle. This load depends on a number of uncertain variables, such as the mass of the vehicle and its speed on impact. The objective of our study is to analyse their effect on the load. More specifically, we are interested in finding the minimum distance of the pillar to the side of the road passing under the bridge such that a given constraint on the load is satisfied in 99% of impact cases, i.e., such that the probability of satisfying the constraint is 0.99. In addition, we look for solutions to the following optimisation problem: find the distance that minimises a given cost function while still satisfying a given constraint on the load. This optimisation problem under uncertain constraints is not a well-posed problem, so we turn it into a decision problem under uncertainty. For both problems, we consider two typical cases. In the first, so-called precise-probability case, all uncertain variables involved are modelled using probability distributions, and in the second, so-called imprecise-probability case, the uncertainty for at least some of the variables (in casu the mass) is modelled by an interval of possible values, which is a special imprecise-probabilistic model. In the first case, we compute the joint distribution using simple Monte Carlo simulation, and in the second case, we combine Monte Carlo simulation with newly developed techniques in the field of imprecise probabilities. For the optimisation problem with uncertain constraints, this leads to two distinct approaches with different optimality criteria, namely maximality and maximinity, which we discuss and compare
Recent advances in imprecise-probabilistic graphical models
We summarise and provide pointers to recent advances in inference and identification for specific types of probabilistic graphical models using imprecise probabilities. Robust inferences can be made in so-called credal networks when the local models attached to their nodes are imprecisely specified as conditional lower previsions, by using exact algorithms whose complexity is comparable to that for the precise-probabilistic counterparts
Maximin and maximal solutions for linear programming problems with possibilistic uncertainty
We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them
The belief noisy-or model applied to network reliability analysis
One difficulty faced in knowledge engineering for Bayesian Network (BN) is
the quan-tification step where the Conditional Probability Tables (CPTs) are
determined. The number of parameters included in CPTs increases exponentially
with the number of parent variables. The most common solution is the
application of the so-called canonical gates. The Noisy-OR (NOR) gate, which
takes advantage of the independence of causal interactions, provides a
logarithmic reduction of the number of parameters required to specify a CPT. In
this paper, an extension of NOR model based on the theory of belief functions,
named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both
aleatory and epistemic uncertainty of the network. Compared with NOR, more rich
information which is of great value for making decisions can be got when the
available knowledge is uncertain. Specially, when there is no epistemic
uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR
are presented in this paper in order to meet various needs of engineers. The
application of BNOR model on the reliability evaluation problem of networked
systems demonstrates its effectiveness
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