Related papers: Justifying the Principle of Interval Constraints

Interval identification of parameters such as average treatment effects, average partial effects and welfare is particularly common when using observational data and experimental data with imperfect compliance due to the endogeneity of…

We address the issue of incorporating a particular yet expressive form of integrity constraints (namely, denial constraints) into probabilistic databases. To this aim, we move away from the common way of giving semantics to probabilistic…

In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…

The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been…

All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…

This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…

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…

There is a growing need for the ability to analyse interval-valued data. However, existing descriptive frameworks to achieve this ignore the process by which interval-valued data are typically constructed; namely by the aggregation of…

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction…

We introduce the problem of ranking with slot constraints, which can be used to model a wide range of application problems -- from college admission with limited slots for different majors, to composing a stratified cohort of eligible…

The Probability Ranking Principle states that the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key point…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

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…

Well-recommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal…

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…