Related papers: On the Simes inequality and its generalization
In this note, we generalize an ancient Greek inequality about the sequence of primes to the cases of arithmetic progressions even multivariable polynomials with integral coefficients. We also refine Bouniakowsky's conjecture [16] and…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
This article discusses the main aspects related to Bell's inequality, both theoretical and experimental. A new derivation of Bell's inequality is also presented, which stands out for its mathematical simplicity. The exposition is mainly…
Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…
This note makes the obvious observation that Hoeffding's original proof of his inequality remains valid in the game-theoretic framework. All details are spelled out for the convenience of future reference.
Certain new inequalities for the sums of factorials are presented.
Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigates. In this work, we follow the proposal…
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…
Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
This paper presents some new inequalities, the most important of which is the inequality given in Theorem 2.1. It can solve a class of inequalities by a unified method. An important application of the inequality given in Theorem 2.1 is to…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We…
This paper analyzes effects of time-dependence in the Bell inequality. A generalized inequality is derived for the case when coincidence and non-coincidence [and hence whether or not a pair contributes to the actual data] is controlled by…
The problem of large-scale simultaneous hypothesis testing is re-visited. Bagging and subagging procedures are put forth with the purpose of improving the discovery power of the tests. The procedures are implemented in both simulated and…
We investigate the simulation problem in of dense-time system. A specification simulates a model if the specification can match every transition that the model can make at a time point. We also adapt the approach of Emerson and Lei and…
Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.
The strengthened data processing inequality have been proved. The general theory have been illustrated on the simple example.