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Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…

The unified approach of Feldman and Cousins allows for exact statistical inference of small signals that commonly arise in high energy physics. It has gained widespread use, for instance, in measurements of neutrino oscillation parameters…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Uncertainty estimation is important for ensuring safety and robustness of AI systems. While most research in the area has focused on un-structured prediction tasks, limited work has investigated general uncertainty estimation approaches for…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…

Data analysis in HEP experiments often uses binned likelihood from data and finite Monte Carlo sample. Statistical uncertainty of Monte Carlo sample has been introduced in Frequentist Inference in some literatures, but they are not suitable…

Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…

We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that 1-\beta' \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha'. We show that this…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

We study the simplifications occurring in any likelihood function in the presence of a large number of small systematic uncertainties. We find that the marginalisation of these uncertainties can be done analytically by means of second-order…

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

We show that the unified method recently proposed by Feldman and Cousins to put confidence intervals on bounded parameters cannot avoid the possibility of getting null results. A modified bayesian approach is also proposed (although not…

Hypothesis tests for the presence of new sources of Poisson counts amidst background processes are frequently performed in high energy physics (HEP), gamma ray astronomy (GRA), and other branches of science. While there are conceptual…

We propose simple randomized strategies for sequential prediction under imperfect monitoring, that is, when the forecaster does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…

Uncertainty quantification, by means of confidence interval (CI) construction, has been a fundamental problem in statistics and also important in risk-aware decision-making. In this paper, we revisit the basic problem of CI construction,…

Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…