Related papers: New Counterexamples for Sums-Differences
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic…
Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single…
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…
As machine learning (ML) models become more widely deployed in high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of…
In this paper, we consider certain finite sums related to the "largest odd divisor", and we obtain, using simple ideas and recurrence relations, sharp upper and lower bounds for these sums.
The aim of this paper is to discuss various concentration inequalities for U-statistics and most recent results. A special focus will be on providing proofs for bounds on the U-statistics using classical concentration inequalities, which,…
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend the result in [11] that square summability of variations of g-functions ensures uniqueness of g-measures. The first…
Some drawbacks of the formalism of Bayes Theorem can be avoided by the rMPE-Method, a modification of the cMPE-Method that permits (i): Adding probabilities in spite of non-linearity. (ii): Taking into account extensional evidence and…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We obtain some inequalities which are stronger than the Schur majorization inequalities.
Measuring uncertainty is a promising technique for detecting adversarial examples, crafted inputs on which the model predicts an incorrect class with high confidence. But many measures of uncertainty exist, including predictive en- tropy…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…