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Uncertainty modelling and conditioning with convex imprecise previsions

Renato Pelessoni, Paolo Vicig
2005 International Journal of Approximate Reasoning  
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

Peter Walley
2000 International Journal of Approximate Reasoning  
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]

Keivan Shariatmadar, Hans Hallez, David Moens
2021 Lecture Notes in Mechanical Engineering  
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

Sebastian Maaß
2008 International Journal of Approximate Reasoning  
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]

Damjan Škulj
2016 arXiv   pre-print
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]

Jasper De Bock, Gert de Cooman
2013 Lecture Notes in Computer Science  
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

Damjan Škulj
2011 International Journal of Approximate Reasoning  
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]

Renato Pelessoni, Paolo Vicig
2004 arXiv   pre-print
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

Paolo Vicig
2008 International Journal of Approximate Reasoning  
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

Keivan Shariatmadar, Adriano Arrigo, François Vallée, Hans Hallez, Lieven Vandevelde, David Moens
2021 Energies  
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

Lala M. Zeinalova, M.A. Mammadova
2016 Procedia Computer Science  
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

INES COUSO, SERAFIN MORAL, PETER WALLEY
2000 Risk, Decision, and Policy  
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

Chiara Corsato, Renato Pelessoni, Paolo Vicig
2017 International Journal of Approximate Reasoning  
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  
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

Lala M Zeinalova
2014 ICTACT Journal on Soft Computing  
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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