12,803 research outputs found
Comparison of experts in the non-additive case
We adapt the model of comparisons of experts initiated by Lehrer («Comparison of experts JME 98») to a context of uncertainty which cannot be modelised by expected utility. We examine the robustness of Lehrer in this new context. Unlike expected utility, there exist several ways to define the strategies allowing to compare the experts, we propose some of them which guarantee a positive value of information.Non-additive preferences, experts
Using graphical models and multi-attribute utility theory for probabilistic uncertainty handling in large systems, with application to nuclear emergency management
Although many decision-making problems involve uncertainty, uncertainty handling within large decision support systems (DSSs) is challenging. One domain where uncertainty handling is critical is emergency response management, in particular nuclear emergency response, where decision making takes place in an uncertain, dynamically changing environment. Assimilation and analysis of data can help to reduce these uncertainties, but it is critical to do this in an efficient and defensible way. After briefly introducing the structure of a typical DSS for nuclear emergencies, the paper sets up a theoretical structure that enables a formal Bayesian decision analysis to be performed for environments like this within a DSS architecture. In such probabilistic DSSs many input conditional probability distributions are provided by different sets of experts overseeing different aspects of the emergency. These probabilities are then used by the decision maker (DM) to find her optimal decision. We demonstrate in this paper that unless due care is taken in such a composite framework, coherence and rationality may be compromised in a sense made explicit below. The technology we describe here builds a framework around which Bayesian data updating can be performed in a modular way, ensuring both coherence and efficiency, and provides sufficient unambiguous information to enable the DM to discover her expected utility maximizing policy
Attitude toward information and learning under multiple priors
This paper studies learning under multiple priors by characterizing the decision maker's attitude toward information. She is incredulous if she integrates new information with respect to only those measures that minimizes the likelihood of the new information and credulous if she uses the maximum likelihood procedure to update her priors. Both updating rules expose her to dynamic inconsistency. We explore different ways to resolve this problem. One way consists to assume that the decision maker's attitude toward information is not relevant to characterize conditional preferences. In this case, we show that a necessary and sufficient condition, introduced by [Epstein L. and Schneider M., 2003. Recursive multiple priors. Journal of Economic Theory 113, 1-31], is the rectangularity of the set of priors. Another way is to extend optimism or pessimism to a dynamic set-up. A pessimistic (max-min expected utility) decision maker will be credulous when learning bad news but incredulous when learning good news.Conversely, an optimistic (max-max expected utility) decision maker will be credulous when learning good news but incredulous when learning bad news. It allows max-min (or max-max) expected utility preferences to be dynamically consistent but it violates consequentialism because conditioning works with respect to counterfactual outcomes. The implications of our findings when the set of priors is the core of a non-additive measure are explored.Multiple priors ; Learning ; Dynamic consistency ; Consequentialism ; Attitude toward information
Envelopes of conditional probabilities extending a strategy and a prior probability
Any strategy and prior probability together are a coherent conditional
probability that can be extended, generally not in a unique way, to a full
conditional probability. The corresponding class of extensions is studied and a
closed form expression for its envelopes is provided. Then a topological
characterization of the subclasses of extensions satisfying the further
properties of full disintegrability and full strong conglomerability is given
and their envelopes are studied.Comment: 2
A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time
In this paper we provide a flexible framework allowing for a unified study of
time consistency of risk measures and performance measures (also known as
acceptability indices). The proposed framework not only integrates existing
forms of time consistency, but also provides a comprehensive toolbox for
analysis and synthesis of the concept of time consistency in decision making.
In particular, it allows for in depth comparative analysis of (most of) the
existing types of time consistency -- a feat that has not be possible before
and which is done in the companion paper [BCP2016] to this one. In our approach
the time consistency is studied for a large class of maps that are postulated
to satisfy only two properties -- monotonicity and locality. The time
consistency is defined in terms of an update rule. The form of the update rule
introduced here is novel, and is perfectly suited for developing the unifying
framework that is worked out in this paper. As an illustration of the
applicability of our approach, we show how to recover almost all concepts of
weak time consistency by means of constructing appropriate update rules
Coherent frequentism
By representing the range of fair betting odds according to a pair of
confidence set estimators, dual probability measures on parameter space called
frequentist posteriors secure the coherence of subjective inference without any
prior distribution. The closure of the set of expected losses corresponding to
the dual frequentist posteriors constrains decisions without arbitrarily
forcing optimization under all circumstances. This decision theory reduces to
those that maximize expected utility when the pair of frequentist posteriors is
induced by an exact or approximate confidence set estimator or when an
automatic reduction rule is applied to the pair. In such cases, the resulting
frequentist posterior is coherent in the sense that, as a probability
distribution of the parameter of interest, it satisfies the axioms of the
decision-theoretic and logic-theoretic systems typically cited in support of
the Bayesian posterior. Unlike the p-value, the confidence level of an interval
hypothesis derived from such a measure is suitable as an estimator of the
indicator of hypothesis truth since it converges in sample-space probability to
1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly
extended to vector parameters of interest. The derivation of upper and lower
confidence levels from valid and nonconservative set estimators is formalize
Exchangeability and sets of desirable gambles
Sets of desirable gambles constitute a quite general type of uncertainty
model with an interesting geometrical interpretation. We give a general
discussion of such models and their rationality criteria. We study
exchangeability assessments for them, and prove counterparts of de Finetti's
finite and infinite representation theorems. We show that the finite
representation in terms of count vectors has a very nice geometrical
interpretation, and that the representation in terms of frequency vectors is
tied up with multivariate Bernstein (basis) polynomials. We also lay bare the
relationships between the representations of updated exchangeable models, and
discuss conservative inference (natural extension) under exchangeability and
the extension of exchangeable sequences.Comment: 40 page
A General Update Rule for Convex Capacities
A characterization of a general update rule for convex capacities, the G-updating rule, is investigated. We introduce a consistency property which bridges between unconditional and conditional preferences, and deduce an update rule for unconditional capacities. The axiomatic basis for the G-updating rule is established through consistent counterfactual acts, which take the form of trinary acts expressed in terms of G, an ordered tripartition of global states.ambiguous belief, Bayes' rule, update rule, convex capacity, Choquet ex- pected utility, conditional preference
- …