The Extension of Imprecise Probabilities Based on Generalized Credal Sets

2016 ◽  
pp. 87-94 ◽  
Author(s):  
Andrey G. Bronevich ◽  
Igor N. Rozenberg
Keyword(s):  
Imprecise Probabilities ◽  
Credal Sets

scholarly journals Risk Assessment of Circuit Breakers Using Influence Diagrams with Interval Probabilities

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 737
Author(s):  
Jelena D. Velimirovic ◽  
Aleksandar Janjic
Keyword(s):  
Power System ◽  
Predictive Modelling ◽  
Optimal Time ◽  
Influence Diagrams ◽  
Circuit Breakers ◽  
Interval Probability ◽  
Complex Power ◽  
Interval Width ◽  
Credal Sets ◽  
The One

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper.

scholarly journals Planning of technical flood retention measures in large river basins under consideration of imprecise probabilities of multivariate hydrological loads

2009 ◽  
Vol 9 (4) ◽  
pp. 1349-1363 ◽  
Author(s):  
D. Nijssen ◽  
A. Schumann ◽  
M. Pahlow ◽  
B. Klein
Keyword(s):  
Flood Control ◽  
Large River ◽  
Control Measures ◽  
Imprecise Probabilities ◽  
Flood Events ◽  
Modeling Tools ◽  
Statistical Characterization ◽  
Design Floods ◽  
Known Unknowns ◽  
Flood Waves

Abstract. As a result of the severe floods in Europe at the turn of the millennium, the ongoing shift from safety oriented flood control towards flood risk management was accelerated. With regard to technical flood control measures it became evident that the effectiveness of flood control measures depends on many different factors, which cannot be considered with single events used as design floods for planning. The multivariate characteristics of the hydrological loads have to be considered to evaluate complex flood control measures. The effectiveness of spatially distributed flood control systems differs for varying flood events. Event-based characteristics such as the spatial distribution of precipitation, the shape and volume of the resulting flood waves or the interactions of flood waves with the technical elements, e.g. reservoirs and flood polders, result in varying efficiency of these systems. Considering these aspects a flood control system should be evaluated with a broad range of hydrological loads to get a realistic assessment of its performance under different conditions. The consideration of this variety in flood control planning design was one particular aim of this study. Hydrological loads were described by multiple criteria. A statistical characterization of these criteria is difficult, since the data base is often not sufficient to analyze the variety of possible events. Hydrological simulations were used to solve this problem. Here a deterministic-stochastic flood generator was developed and applied to produce a large quantity of flood events which can be used as scenarios of possible hydrological loads. However, these simulations imply many uncertainties. The results will be biased by the basic assumptions of the modeling tools. In flood control planning probabilities are applied to characterize uncertainties. The probabilities of the simulated flood scenarios differ from probabilities which would be derived from long time series. With regard to these known unknowns the bias of the simulations was considered by imprecise probabilities. Probabilities, derived from measured flood data were combined with probabilities which were estimated from long simulated series. To consider imprecise probabilities, fuzzy sets were used to distinguish the results between more or less possible design floods. The need for such a differentiated view on the performance of flood protection systems is demonstrated by a case study.

A Modified Supervaluationist Framework for Decision-Making

2021 ◽  
Vol 12 (2) ◽  
pp. 175-191
Author(s):  
Jonas Karge ◽  
Keyword(s):  
Decision Making ◽  
Probability Function ◽  
Imprecise Probabilities ◽  
Adequate Account ◽  
Alternative Account ◽  
Semantic Approach ◽  
Probability Functions ◽  
Degree Of Belief ◽  
The Way

How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be manifested in decision-making. In response to Elga, more elaborate accounts of the imprecise framework have been developed. One of them is based on supervaluationism, originally, a semantic approach to vague predicates. Still, Seamus Bradley shows that some of those accounts that solve Elga’s problem, have a more severe defect: they undermine a central motivation for introducing imprecise probabilities in the first place. In this paper, I modify the supervaluationist approach in such a way that it accounts for both Elga’s and Bradley’s challenges to the imprecise framework.

Conciliatory Views on Peer Disagreement and the Order of Evidence Acquisition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Marc Andree Weber
Keyword(s):  
Belief Revision ◽  
Point Of View ◽  
Imprecise Probabilities ◽  
Peer Disagreement

Abstract The evidence that we get from peer disagreement is especially problematic from a Bayesian point of view since the belief revision caused by a piece of such evidence cannot be modelled along the lines of Bayesian conditionalisation. This paper explains how exactly this problem arises, what features of peer disagreements are responsible for it, and what lessons should be drawn for both the analysis of peer disagreements and Bayesian conditionalisation as a model of evidence acquisition. In particular, it is pointed out that the same characteristic of evidence from disagreement that explains the problems with Bayesian conditionalisation also suggests an interpretation of suspension of belief in terms of imprecise probabilities.

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