Related papers: On Missing Mass Variance
We consider studies where multiple measures on an outcome variable are collected over time, but some subjects drop out before the end of follow up. Analyses of such data often proceed under either a 'last observation carried forward' or…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…
We are interested in the behavior of particular functionals, in a framework where the only source of randomness is a sampling without replacement. More precisely the aim of this short note is to prove an exponential concentration inequality…
A mixture with varying concentrations is a modification of a finite mixture model in which the mixing probabilities (concentrations of mixture components) may be different for different observations. In the paper, we assume that the…
Multiple matrix sampling is a survey methodology technique that randomly chooses a relatively small subset of items to be presented to survey respondents for the purpose of reducing respondent burden. The data produced are missing…
A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Let $P=(x_1,\ldots,x_n)$ be a population consisting of $n\ge 2$ real numbers whose sum is zero, and let $k <n$ be a positive integer. We sample $k$ elements from $P$ without replacement and denote by $X_P$ the sum of the elements in our…
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…
Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work…
Mass loss rate formulae are derived from observations or from suites of models. For theoretical models, the following have all been identified as factors greatly influencing the atmospheric structure and mass loss rates: Pulsation with…
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like…