Related papers: Multivariate Confidence Intervals
This research introduces a new constraint domain for reasoning about data with uncertainty. It extends convex modeling with the notion of p-box to gain additional quantifiable information on the data whereabouts. Unlike existing approaches,…
Intervals are a popular way to represent the uncertainty related to data, in which we express the vagueness of each observation as the width of the interval. However, when using intervals for this purpose, we need to use the appropriate set…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
A calculator program has been written to give confidence intervals on branching ratios for rare decay modes (or similar quantities) calculated from the number of events observed, the acceptance factor, the background estimate and the…
Machine learning models are increasingly used to produce predictions that serve as input data in subsequent statistical analyses. For example, computer vision predictions of economic and environmental indicators based on satellite imagery…
In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity…
Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…
The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…
Consider a linear regression model with independent and identically normally distributed random errors. Suppose that the parameter of interest is a specified linear combination of the regression parameters. We prove that the usual…
It is common when using cross-section or panel data to assign each observation to a cluster and allow for arbitrary patterns of heteroskedasticity and correlation within clusters. For regression models, there are many ways to make…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
The aim of this paper is to firmly establish subjective fiducial inference as a rival to the more conventional schools of statistical inference, and to show that Fisher's intuition concerning the importance of the fiducial argument was…
Given a pair of multivariate time-series data of the same length and dimensions, an approach is proposed to select variables and time intervals where the two series are significantly different. In applications where one time series is an…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
Displaying confidence scores in human-AI interaction has been shown to help build trust between humans and AI systems. However, most existing research uses only the confidence score as a form of communication. As confidence scores are just…
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…
The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but…
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the…