Related papers: Robust Estimation of Mean Values
Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…
In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a…
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system. The quantification of the…
Suppose that $X_1,X_2,\ldots$ are a stream of independent, identically distributed Poisson random variables with mean $\mu$. This work presents a new estimate $\mu_k$ for $\mu$ with the property that the distribution of the relative error…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
Uncertainty requires suitable techniques for risk assessment. Combining stochastic approximation and stochastic average approximation, we propose an efficient algorithm to compute the worst case average value at risk in the face of tail…
Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…
Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…
Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample…
The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to…