Related papers: Confidence Intervals for Unobserved Events

We consider the estimation of rare-event probabilities using sample proportions output by naive Monte Carlo or collected data. Unlike using variance reduction techniques, this naive estimator does not have a priori relative efficiency…

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.…

The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the…

Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported…

Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including health care, astronomy, and climate. State-of-the-art methods for the task estimate only…

We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…

Although the interest in the the use of social and information networks has grown, most inferences on networks assume the data collected represents the complete. However, when ignoring missing data, even when missing completely at random,…

In this paper, we have established a unified framework of multistage parameter estimation. We demonstrate that a wide variety of statistical problems such as fixed-sample-size interval estimation, point estimation with error control,…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…

This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified…

Accounting for both rare events and complex sampling presents challenges when quantifying uncertainty for rate estimation in autonomous vehicle performance evaluation. In this paper, we introduce a statistical formulation of this problem…

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of…

In the era of fast-paced precision medicine, observational studies play a major role in properly evaluating new treatments in clinical practice. Yet, unobserved confounding can significantly compromise causal conclusions drawn from…

This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that…

In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid…