Related papers: Non-deterministic inference using random set model…

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

This article is an extension of the results of two earlier articles. In [J. Schubert, On nonspecific evidence, Int. J. Intell. Syst. 8 (1993) 711-725] we established within Dempster-Shafer theory a criterion function called the metaconflict…

In recent years, researchers in decision analysis and artificial intelligence (Al) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions,…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets,…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…

We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

The inferential model (IM) framework produces data-dependent, non-additive degrees of belief about the unknown parameter that are provably valid. The validity property guarantees, among other things, that inference procedures derived from…

Efficient modeling of uncertain information in real world is still an open issue. Dempster-Shafer evidence theory is one of the most commonly used methods. However, the Dempster-Shafer evidence theory has the assumption that the hypothesis…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of…