Related papers: Inference for bounded parameters
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
This paper introduces a general theoretical framework to analyze noise limited networks. More precisely, we consider two homogenous Poisson point processes of base stations and users. General model of radio signal propagation and effect of…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
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…
This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…
Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…
We present a rigorous description of the general problem of aperture photometry in high energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
In particle physics and cosmology, distinguishing subtle new physics signals from established backgrounds is a fundamental and persistent challenge for phenomenologists. This paper discuss a simple and robust statistical framework to…
A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order…