Related papers: On upper and lower bounds for probabilities of com…
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
Let $A_1, A_2, \ldots, A_n$ be events in a sample space. Given the probability of the intersection of each collection of up to $k+1$ of these events, what can we say about the probability that at least $r$ of the events occur? This question…
A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $P\left(\bigcup_{i=1}^N A_i\right)$, in terms of the individual event probabilities $\{P(A_i), i=1,\ldots,N\}$ and the sums of the pairwise…
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…
This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set $A$, when the prior lies in a class of probability measures $\mathcal{P}$ and the likelihood is precise.…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
Given a set of probability measures $\mathcal{P}$ representing an agent's knowledge on the elements of a sigma-algebra $\mathcal{F}$, we can compute upper and lower bounds for the probability of any event $A\in\mathcal{F}$ of interest. A…
We establish bounds on the probability that two different agents, who share an initial opinion expressed as a probability distribution on an abstract probability space, given two different sources of information, may come to radically…
When backgrounds are not well enough controlled to measure the value of some physical parameter, one may still obtain an upper limit on the parameter. A single experiment may have several detectors, each of which can alone be used to derive…
We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations.…
In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…
In this paper, we consider several types of information and methods of combination associated with incomplete probabilistic systems. We discriminate between 'a priori' and evidential information. The former one is a description of the whole…
We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…