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There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…
This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and…
We consider the Last-Success-Problem with $n$ independent Bernoulli random variables with parameters $p_i>0$. We improve the lower bound provided by F.T. Bruss for the probability of winning and provide an alternative proof to the one given…
When estimating a proportion and only a sample of triplets is given, dependencies within the triplets are to be accounted for. Without assuming a distribution for the success count of the triplet, together with the proportion, as second and…
We consider Empirical Bayes (EB) estimation in the normal means problem, when the standard deviations of the observations are not known precisely, but estimated with error -- which is almost always the case in practical applications. In…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
A popular setting in medical statistics is a group sequential trial with independent and identically distributed normal outcomes, in which interim analyses of the sum of the outcomes are performed. Based on a prescribed stopping rule, one…
Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge…
In this article, we study the approximation of a probability measure $\mu$ on $\mathbb{R}^{d}$ by its empirical measure $\hat{\mu}_{N}$ interpreted as a random quantization. As error criterion we consider an averaged $p$-th moment…
This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…
In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
We calculate the exact subgaussian norm of a centered (shifted) indicator (Bernoulli's) random variable. Using this result we derive very simple tail estimates for sums of these variables, not necessary to be identical distributed, and give…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…
Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
We consider a problem of statistical mean estimation in which the samples are not observed directly, but are instead observed by a relay (``teacher'') that transmits information through a memoryless channel to the decoder (``student''), who…