Related papers: Multiscale probability transformation of basic pro…

Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…

We provide frequency probabilistic analysis of perturbations of physical systems by preparation procedures. We obtained the classification of possible probabilistic transformations connecting input and output probabilities that can appear…

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…

In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…

Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. We need evidence to support that the resulting decisions are well-founded. To aid development of trust in these decisions,…

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…

Bayesian inference as applied in a legal setting is about belief transfer and involves a plurality of agents and communication protocols. A forensic expert (FE) may communicate to a trier of fact (TOF) first its value of a certain…

Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…

When reasoning with uncertainty there are many situations where evidences are not only uncertain but their propositions may also be weakly specified in the sense that it may not be certain to which event a proposition is referring. It is…

Mathematical Theory of Evidence called also Dempster-Shafer Theory (DST) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its…

By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…

This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use…

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…

We develop our interpretation of the joint belief distribution and of evidential updating that matches the following basic requirements: * there must exist an efficient method for reasoning within this framework * there must exist a clear…

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal…

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…

Language modeling has shifted in recent years from a distribution over strings to prediction models with textual inputs and outputs for general-purpose tasks. This position paper highlights the often overlooked implications of this shift…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can…

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…