Related papers: Fiducial on a string
Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
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…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the…
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect") , but recent experiments varying the speed and order of…
Without assuming any pdf for some measured parameter, we derive a predictive pdf for the outcome of a second measurement, given the outcome of the first measurement and two common assumptions about the noise. These are that (1) it is…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…
A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist)…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
For the usual normal approximations to binomial, hypergeometric, or Poisson interval probabilities, we collect some simple but then reasonably sharp error bounds. For the Clopper-Pearson~(1934) binomial confidence bounds, we present,…
R. A. Fisher introduced the fiducial distribution as a potential replacement for the Bayesian posterior distribution in the 1930s. During the past century, fiducial approaches have been explored in various parametric and nonparametric…
The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties: First, it…
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…