相关论文: Asymmetric Uncertainties: Sources, Treatment and P…

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…

There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…

In distributed systems with asymmetric trust, each participant is free to make its own trust assumptions about others, captured by an asymmetric quorum system. This contrasts with ordinary, symmetric quorum systems and threshold models,…

Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to…

Bad statistics make research papers unreproducible and misleading. For the most part, the reasons for such misusage of numerical data have been found and addressed years ago by experts and proper practical solutions have been presented…

We consider the problem of filtering an unseen Markov chain from noisy observations, in the presence of uncertainty regarding the parameters of the processes involved. Using the theory of nonlinear expectations, we describe the uncertainty…

Measuring uncertainties in the output of a deep learning method is useful in several ways, such as in assisting with interpretation of the outputs, helping build confidence with end users, and for improving the training and performance of…

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:…

Uncertainty estimation, which provides a means of building explainable neural networks for medical imaging applications, have mostly been studied for single deep learning models that focus on a specific task. In this paper, we propose a…

A general mathematical derivation is given of the uncertainty arising from photon statistics in spectroscopic determination of line shift and width, in the presence of a background spectrum.

In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…

We review the reasoning underlying two approaches to combination of sensory uncertainties. First approach is noncommittal, making no assumptions about properties of uncertainty or parameters of stimulation. Then we explain the relationship…

We propose here selected actual features of measurement problems based on our concerns in our respective fields of research. Their technical similarity in apparently disconnected fields motivate this common communication. Problems of…

The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…

This paper analyzes nonlinearities in the international transmission of financial shocks originating in the US. To do so, we develop a flexible nonlinear multi-country model. Our framework is capable of producing asymmetries in the…

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…

We live in unprecedented times in terms of our ability to use evidence to inform medical care. For example, we can perform data-driven post-test probability calculations. However, there is work to do. As has been previously noted,…