Results 1  10
of
855
Measuring Expectations
, 2004
"... This article discusses the history underlying the new literature, describes some of what has been learned thus far, and looks ahead towards making further progress ..."
Abstract

Cited by 168 (11 self)
 Add to MetaCart
This article discusses the history underlying the new literature, describes some of what has been learned thus far, and looks ahead towards making further progress
Game Theory, Maximum Entropy, Minimum Discrepancy And Robust Bayesian Decision Theory
 ANNALS OF STATISTICS
, 2004
"... ..."
Artificial Reasoning with Subjective Logic
, 1997
"... This paper defines a framework for artificial reasoning called Subjective Logic, which consists of a belief model called opinion and set of operations for combining opinions. Subjective Logic is an extension of standard logic that uses continuous uncertainty and belief parameters instead of only ..."
Abstract

Cited by 47 (11 self)
 Add to MetaCart
(Show Context)
This paper defines a framework for artificial reasoning called Subjective Logic, which consists of a belief model called opinion and set of operations for combining opinions. Subjective Logic is an extension of standard logic that uses continuous uncertainty and belief parameters instead of only discrete truth values. It can also be seen as an extension of classical probability calculus by using a second order probability representation instead of the standard first order representation. In addition to the standard logical operations, Subjective Logic contains some operations specific for belief theory such as consensus and recommendation. In particular, we show that Dempster's consensus rule is inconsistent with Bayes' rule and therefore is wrong, and provide an alternative rule with a solid mathematical basis. Subjective Logic is directly compatible with traditional mathematical frameworks, but is also suitable for handling ignorance and uncertainty which is required in artificial...
Towards a unified theory of imprecise probability
 Int. J. Approx. Reasoning
, 2000
"... Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to ..."
Abstract

Cited by 45 (0 self)
 Add to MetaCart
(Show Context)
Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to represent some common types of uncertainty. Coherent lower previsions and sets of probability measures are considerably more general but they may not be sufficiently informative for some purposes. I discuss two other models for uncertainty, involving sets of desirable gambles and partial preference orderings. These are more informative and more general than the previous models, and they may provide a suitable mathematical setting for a unified theory of imprecise probability.
Practical Representation of Incomplete Probabilistic Information
 Advances in Soft Computing:Soft Methods of Probability and Statistics conference
, 2004
"... This article deals with the compact representation of incomplete probabilistic knowledge which can be encountered in risk evaluation problems, for instance in environmental studies. Various kinds of knowledge are considered such as expert opinions about characteristics of distributions or poor stati ..."
Abstract

Cited by 39 (13 self)
 Add to MetaCart
(Show Context)
This article deals with the compact representation of incomplete probabilistic knowledge which can be encountered in risk evaluation problems, for instance in environmental studies. Various kinds of knowledge are considered such as expert opinions about characteristics of distributions or poor statistical information. Our approach is based on probability families encoded by possibility distributions and belief functions. In each case, a technique for representing the available imprecise probabilistic information faithfully is proposed, using different uncertainty frameworks (possibility theory, probability theory, belief functions...). Moreover the use of probabilitypossibility transformations enables confidence intervals to be encompassed by cuts of possibility distributions, thus making the representation stronger. The respective appropriateness of pairs of cumulative distributions, continuous possibility distributions or discrete random sets for representing information about the mean value, the mode, the median and other fractiles of illknown probability distributions is discussed in detail.
Supremum Preserving Upper Probabilities
, 1998
"... We study the relation between possibility measures and the theory of imprecise probabilities, and argue that possibility measures have an important part in this theory. It is shown that a possibility measure is a coherent upper probability if and only if it is normal. A detailed comparison is giv ..."
Abstract

Cited by 38 (13 self)
 Add to MetaCart
We study the relation between possibility measures and the theory of imprecise probabilities, and argue that possibility measures have an important part in this theory. It is shown that a possibility measure is a coherent upper probability if and only if it is normal. A detailed comparison is given between the possibilistic and natural extension of an upper probability, both in the general case and for upper probabilities dened on a class of nested sets. We prove in particular that a possibility measure is the restriction to events of the natural extension of a special kind of upper probability, dened on a class of nested sets. We show that possibilistic extension can be interpreted in terms of natural extension. We also prove that when either the upper or the lower cumulative distribution function of a random quantity is specied, possibility measures very naturally emerge as the corresponding natural extensions. Next, we go from upper probabilities to upper previsions...
Learning under Ambiguity
 Review of Economic Studies
, 2002
"... This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extremeit models agents who are implausibly ambitious about w ..."
Abstract

Cited by 35 (4 self)
 Add to MetaCart
(Show Context)
This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extremeit models agents who are implausibly ambitious about what they can learn in complicated environments. The paper then provides a generalization of the Bayesian model that accommodates the intuitive choices in the thought experiments. In particular, the model allows decisionmakers ’ confidence about the environment to change — along with beliefs — as they learn. A portfolio choice application compares the effect of changes in confidence under ambiguity versus changes in estimation risk under Bayesian learning. The former is shown to induce a trend towards more stock market participation and investment even when the latter does not. 1
Data Fusion in the Transferable Belief Model.
, 2000
"... When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster's rule of combination have been produced and the meaning of ..."
Abstract

Cited by 35 (0 self)
 Add to MetaCart
When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster's rule of combination have been produced and the meaning of distinctness has been assessed. We will present practical applications where the fusion of uncertain data is well achieved by Dempster's rule of combination. It is essential that the meaning of the belief functions used to represent uncertainty be well fixed, as the adequacy of the rule depends strongly on a correct understanding of the context in which they are applied. Missing to distinguish between the upper and lower probabilities theory and the transferable belief model can lead to serious confusion, as Dempster's rule of combination is central in the transferable belief model whereas it hardly fits with the upper and lower probabilities theory. Keywords: belief function, transferable beli...