Related papers: Random sets and exact confidence regions

In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…

The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic…

Relative surprise regions are shown to minimize, among Bayesian credible regions, the prior probability of covering a false value from the prior. Such regions are also shown to be unbiased in the sense that the prior probability of covering…

In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…

This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical…

We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…

In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an…

Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for…

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…

Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through…

This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…

A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…

Estimating the mode of a unimodal distribution is a classical problem in statistics. Although there are several approaches for point-estimation of mode in the literature, very little has been explored about the interval-estimation of mode.…

Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…

Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…

In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…

Confidence intervals are central to statistical inference as a tool to evaluate the type I error risk at a given significance level. We devise a method to construct confidence intervals using a single run of a permutation test. This…

While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…