Related papers: A Remark on the Structure of Expectiles
The standard conditional probability definition formula is derived as a consequence of the Insufficient Reason Principle expressed as the Maximum Relative Divergence Principle for grading (order-comonotonic) functions on a totally ordered…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
In the paper we argue that performance of the classifiers based on Empirical Risk Minimization (ERM) for positive unlabeled data, which are designed for case-control sampling scheme may significantly deteriorate when applied to a…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…
We study elementary theories of well-pointed toposes and pretoposes, regarded as category-theoretic or "structural" set theories in the spirit of Lawvere's "Elementary Theory of the Category of Sets". We consider weak intuitionistic and…
We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk…
The Improbability Scale (IS) is proposed as a way of communicating to the general public the improbability (and by implication, the probability) of events predicted as the result of scientific research. Through the use of the Improbability…
The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and…
We define susceptibilities as a measure of the response of an observable quantity of a parameterized statistical model to a perturbation of the data for a general class of observables. We define estimators for these susceptibilities as…
Several interesting models for contingency tables are defined by a system of equality and inequality constraints on a suitable set of marginal log-linear parameters. After reviewing the most common difficulties which are intrinsic to order…
Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…
The insight that causal parameters are particularly suitable for out-of-sample prediction has sparked a lot development of causal-like predictors. However, the connection with strict causal targets, has limited the development with good…
In this article we define a special class of weak expectations for a representation of a separable unital C*-algebra, called decomposable weak expectation. We give necessary and sufficient conditions for such kind of weak expectations to…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…