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Uncertainty modelling and conditioning with convex imprecise previsions
2005
International Journal of Approximate Reasoning
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Convexity further provides a conceptual framework for some uncertainty models and devices, like unnormalised supremum preserving functions. ...
Two classes of imprecise previsions, which we termed convex and centered convex previsions, are studied in this paper in a framework close to WalleyÕs and WilliamsÕ theory of imprecise previsions. ...
framework for some uncertainty models. ...
doi:10.1016/j.ijar.2004.10.007
fatcat:mbbrvsfqi5b4joztxyjjvdlyee
Towards a unified theory of imprecise probability
2000
International Journal of Approximate Reasoning
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In particular, they are not suciently informative about expectations and conditional probabilities. ...
These are more informative and more general than the previous models, and they may provide a suitable mathematical foundation for a uni®ed theory of imprecise probability. ...
Acknowledgements I want to thank FAPESP and the Escola Polit ecnica, Universidade de São Paulo, for supporting this research. ...
doi:10.1016/s0888-613x(00)00031-1
fatcat:b3l5nkmdgbgjtaxkcvivcg3zui
Identification of Imprecision in Data Using $$\epsilon $$-Contamination Advanced Uncertainty Model
[chapter]
2021
Lecture Notes in Mechanical Engineering
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In the second approach, we calculate the lowest and highest previsions for the test function and identify the imprecision interval out of them. ...
AbstractOne of the importance of the contamination uncertainty model is to consider in-determinism in the uncertainty. We consider this advanced property and develop two methods. ...
Definition -contamination model P (·) is described as a convex combination of two uncertainty models: (i) linear prevision model-Probabilistic model, e.g., Normal distributed model E, and (ii) lower prevision ...
doi:10.1007/978-3-030-77256-7_14
fatcat:rzuyoc2j65co7gszj6b2tth77a
Coherent and convex fair pricing and variability measures
2008
International Journal of Approximate Reasoning
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In this paper, we show that coherent upper and lower previsions as well as coherent risk measures are only meaningful under the assumption that one starts with initial wealth being constantly 0. ...
selling prices and coherent lower previsions represent fair prices. ...
Financial support by Credit Suisse and the National Centre of Competence in Research ''Financial Valuation and Risk Management'' (NCCR FINRISK) is gratefully acknowledged. ...
doi:10.1016/j.ijar.2007.06.010
fatcat:x23lnckqjfdwxpkb4oxm56evze
Perturbation bounds and degree of imprecision for uniquely convergent imprecise Markov chains
[article]
2016
arXiv
pre-print
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We provide the maximal distance between the distributions of original and perturbed chain and maximal degree of imprecision, given the imprecision of the initial distribution. ...
The bounds on the errors and degrees of imprecision are found for the distributions at finite time steps, and for the stationary distributions as well. ...
Mitrophanov for his helpful suggestions and discussions. ...
arXiv:1602.08901v1
fatcat:coiztt6t6fe4vhuhfdhd63liqu
Extreme Lower Previsions and Minkowski Indecomposability
[chapter]
2013
Lecture Notes in Computer Science
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Keywords: Extreme lower previsions, extreme credal sets, fully imprecise lower previsions, fully imprecise credal sets, Minkowski decomposition. 1 N denotes the positive integers (excluding zero) and R ...
Indeed, a variable that can only assume a single value has no uncertainty associated with it. ...
Fellow of the Fund for Scientific Research -Flanders (FWO) and wishes to acknowledge its financial support. The authors also wish to thank three anonymous referees for their helpful comments. ...
doi:10.1007/978-3-642-39091-3_14
fatcat:j7q2falkefdnlpzoxxkzacg6oy
The use of Markov operators to constructing generalised probabilities
2011
International Journal of Approximate Reasoning
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It is based on the models using lower and upper previsions, or equivalently, convex sets of probability measures. ...
Imprecise probability models are then obtained in the ways to be consistent with those desirability preserving rules. ...
Acknowledgement I thank the referees for their valuable comments and suggestions that helped me to improve this paper. ...
doi:10.1016/j.ijar.2011.08.001
fatcat:hnn74k6qbfcabe47gzc6ikxr2a
Convex Imprecise Previsions: Basic Issues and Applications
[article]
2004
arXiv
pre-print
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Convexity further provides a conceptual framework for some uncertainty models and devices, like unnormalised supremum preserving functions. ...
In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley's theory of imprecise previsions. ...
framework for some uncertainty models. ...
arXiv:math/0412030v1
fatcat:qxn26yqyt5fwfcz7szylq3msua
Financial risk measurement with imprecise probabilities
2008
International Journal of Approximate Reasoning
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Shortfall-based measures and Dutch risk measures are also investigated. Further, conditional risks can be measured by introducing conditional convex previsions. ...
This analysis also makes us consider a very large class of imprecise previsions, which we termed convex previsions, generalizing convex risk measures. ...
Acknowledgements I am grateful to Teddy Seidenfeld and the Steering Committee of ISIPTA'05 for inviting me to deliver a tutorial talk on imprecise probabilities in risk measurement, and to Fabio Cozman ...
doi:10.1016/j.ijar.2007.06.009
fatcat:xcyge6oelrgpxnevpzc7zg7xg4
Day-Ahead Energy and Reserve Dispatch Problem under Non-Probabilistic Uncertainty
2021
Energies
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In this paper, the aim is to apply two advanced non-probabilistic uncertainty models: Interval and ϵ-contamination, where the imprecision and in-determinism in the uncertainty (uncertain parameters) are ...
Nevertheless, these classical models are not valid when the uncertainty is imprecise, meaning that the system operator may not rely on a unique distribution function to describe the uncertainty. ...
To measure and quantify the 400 imprecise uncertainty we use (coherent) lower & upper previsions which is one 401 of the advanced measures to deal with the imprecision. ...
doi:10.3390/en14041016
fatcat:27febsh2uzbxzmhwi2e3daglle
Decision Making on Oil Extraction under Z-information
2016
Procedia Computer Science
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The method associates with the construction of a non-additive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function. ...
Therefore, the process of oil production takes place in conditions of uncertainty accompanying the various situations. ...
These subsets satisfy the conditions of normality, convexity, and are upper semicontinuous with compact support. Let , n V W E . ...
doi:10.1016/j.procs.2016.09.385
fatcat:wemnp5mhqrbhlbicne7crry7oa
A survey of concepts of independence for imprecise probabilities
2000
Risk, Decision, and Policy
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With this aim, simple examples are given in order to clarify the meaning of the different concepts of independence and the relationships between them. ...
In this paper we try to clarify the notion of independence for imprecise probabilities. ...
The authors thank Fabio Cozman and two referees for helpful comments. ...
doi:10.1017/s1357530900000156
fatcat:gkqpckodczgvldtnv26mquoeha
Weak Dutch Books with imprecise previsions
2017
International Journal of Approximate Reasoning
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Uncertainty assessments for imprecise previsions based on coherence and related concepts require that the suprema of certain random numbers (interpreted as gains) are non-negative. ...
for conditional (Williams') coherent lower previsions. ...
Pelessoni and P. Vicig acknowledge partial support by the FRA2015 grant 'Mathematical Models for Handling Risk and Uncertainty'. ...
doi:10.1016/j.ijar.2017.05.004
fatcat:ekmcuu2fpzf7lelws6kl6qokee
Page 7213 of Mathematical Reviews Vol. , Issue 2004i
[page]
2004
Mathematical Reviews
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The broader class of convex imprecise previsions is also studied and its fundamental properties are demonstrated, introducing in particular a notion of convex natural extension which parallels that of ...
Friedrich Liese (D-ROST; Rostock)
2004i:62037 62F07 62A01 Pelessoni, Renato (I-TRST-A; Trieste) ; Vicig, Paolo (I-TRST-A; Trieste) Convex imprecise previsions. ...
CHOQUET AGGREGATION BASED DECISION MAKING UNDER Z-INFORMATION
2014
ICTACT Journal on Soft Computing
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The concept of decision making under uncertainty is usually associated with information that may be incomplete, not reliable or imprecise, so there are several types of uncertainty. ...
The method associates with the construction of a non-additive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function. ...
These subsets satisfy the conditions of normality, convexity, and are upper semicontinuous with compact support. Let n W V , . ...
doi:10.21917/ijsc.2014.0117
fatcat:z2f6lmvoenbg3owyh764gul3l4
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