Related papers: A Theory of Uncertainty Variables for State Estima…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
Assessing the predictive uncertainty of deep neural networks is crucial for safety-related applications of deep learning. Although Bayesian deep learning offers a principled framework for estimating model uncertainty, the common approaches…
Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty…
Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…
A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing conditional distributions. The parameters are viewed as random variables to…
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…
Although there are many mathematical theories to address uncertain phenomena however, these theories are presented under implicit presupposition that uncertainty of objects is accurately measurable while not considering that the measure of…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…
The problem of estimating event truths from conflicting agent opinions in a social network is investigated. An autoencoder learns the complex relationships between event truths, agent reliabilities and agent observations. A Bayesian network…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
The superstatistics approach recently introduced by Beck [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a unifying way with a large variety of complex nonequilibrium systems, for which…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…
We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…