28 research outputs found
A Cantelli-type inequality for constructing non-parametric p-boxes based on exchangeability.
In this paper we prove a new probability inequality that
can be used to construct p-boxes in a non-parametric
fashion, using the sample mean and sample standard
deviation instead of the true mean and true standard deviation.
The inequality relies only on exchangeability
and boundedness
Sklar's theorem in an imprecise setting
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision
Constructing copulas from shock models with imprecise distributions
The omnipotence of copulas when modeling dependence given marg\-inal
distributions in a multivariate stochastic situation is assured by the Sklar's
theorem. Montes et al.\ (2015) suggest the notion of what they call an
\emph{imprecise copula} that brings some of its power in bivariate case to the
imprecise setting. When there is imprecision about the marginals, one can model
the available information by means of -boxes, that are pairs of ordered
distribution functions. By analogy they introduce pairs of bivariate functions
satisfying certain conditions. In this paper we introduce the imprecise
versions of some classes of copulas emerging from shock models that are
important in applications. The so obtained pairs of functions are not only
imprecise copulas but satisfy an even stronger condition. The fact that this
condition really is stronger is shown in Omladi\v{c} and Stopar (2019) thus
raising the importance of our results. The main technical difficulty in
developing our imprecise copulas lies in introducing an appropriate stochastic
order on these bivariate objects
Addressing ambiguity in randomized reinsurance stop-loss treaties using belief functions
The aim of the paper is to model ambiguity in a randomized reinsurance stop-loss treaty. For this, we consider the lower envelope of the set of bivariate joint probability distributions having a precise discrete marginal and an ambiguous Bernoulli marginal. Under an independence assumption, since the lower envelope fails 2-monotonicity, inner/outer Dempster-Shafer approximations are considered, so as to select the optimal retention level by maximizing the lower expected insurer's annual profit under reinsurance. We show that the inner approximation is not suitable in the reinsurance problem, while the outer approximation preserves the given marginal information, weakens the independence assumption, and does not introduce spurious information in the retention level selection problem. Finally, we provide a characterization of the optimal retention level
A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts
This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email.
The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework
A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts
This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs
with individual (and consensual group) decision making and action based on belief awareness. Comments and
criticisms are most welcome via email.
Starting with a thorough discussion of the conceptual embedding in existing schools of thought and liter-
ature we develop a framework that aims to be empirically adequate yet scalable to epistemic states where an
agent might testify to uncertainly believe a propositional formula based on the acceptance that a propositional
formula is possible, called accepted truth. The familiarity of human agents with probability assignments make
probabilism particularly appealing as quantitative modelling framework for defeasible reasoning that aspires
empirical adequacy for gradual belief expressed as credence functions. We employ the inner measure induced
by the probability measure, going back to Halmos, interpreted as estimate for uncertainty. Doing so omits
generally requiring direct probability assignments testi�ed as strength of belief and uncertainty by a human
agent. We provide a logical setting of the two concepts uncertain belief and accepted truth, completely relying
on the the formal frameworks of 'Reasoning about Probabilities' developed by Fagin, Halpern and Megiddo and
the 'Metaepistemic logic MEL' developed by Banerjee and Dubois. The purport of Probabilistic Uncertainty is
a framework allowing with a single quantitative concept (an inner measure induced by a probability measure)
expressing two epistemological concepts: possibilities as belief simpliciter called accepted truth, and the agents'
credence called uncertain belief for a criterion of evaluation, called rationality. The propositions accepted to be
possible form the meta-epistemic context(s) in which the agent can reason and testify uncertain belief or suspend
judgement
A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts
This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs
with individual (and consensual group) decision making and action based on belief awareness. Comments and
criticisms are most welcome via email.
Starting with a thorough discussion of the conceptual embedding in existing schools of thought and liter-
ature we develop a framework that aims to be empirically adequate yet scalable to epistemic states where an
agent might testify to uncertainly believe a propositional formula based on the acceptance that a propositional
formula is possible, called accepted truth. The familiarity of human agents with probability assignments make
probabilism particularly appealing as quantitative modelling framework for defeasible reasoning that aspires
empirical adequacy for gradual belief expressed as credence functions. We employ the inner measure induced
by the probability measure, going back to Halmos, interpreted as estimate for uncertainty. Doing so omits
generally requiring direct probability assignments testi�ed as strength of belief and uncertainty by a human
agent. We provide a logical setting of the two concepts uncertain belief and accepted truth, completely relying
on the the formal frameworks of 'Reasoning about Probabilities' developed by Fagin, Halpern and Megiddo and
the 'Metaepistemic logic MEL' developed by Banerjee and Dubois. The purport of Probabilistic Uncertainty is
a framework allowing with a single quantitative concept (an inner measure induced by a probability measure)
expressing two epistemological concepts: possibilities as belief simpliciter called accepted truth, and the agents'
credence called uncertain belief for a criterion of evaluation, called rationality. The propositions accepted to be
possible form the meta-epistemic context(s) in which the agent can reason and testify uncertain belief or suspend
judgement
A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts
This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email.
The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework