Related papers: Statistical inference with belief functions: A sur…

Parameter estimation based on uncertain data represented as belief structures is one of the latest problems in the Dempster-Shafer theory. In this paper, a novel method is proposed for the parameter estimation in the case where belief…

Existing frameworks for probabilistic inference assume the quantity of interest is the parameter of a posited statistical model. In machine learning applications, however, often there is no statistical model/parameter; the quantity of…

The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into…

In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and consequently it is important to understand the effects of misspecification on inferential procedures. When the hypothesized…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…

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…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical…

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…

Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…

Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works…

This paper addresses the problem of defining a subjective interestingness measure for BI exploration. Such a measure involves prior modeling of the belief of the user. The complexity of this problem lies in the impossibility to ask the user…

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…

This paper clarifies a fundamental difference between causal inference and traditional statistical inference by formalizing a mathematical distinction between their respective parameters. We connect two major approaches to causal inference,…

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…

The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing…

A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to…

Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…

We first show that there are practical situations in for instance forensic and gambling settings, in which applying classical probability theory, that is, based on the axioms of Kolmogorov, is problematic. We then introduce and discuss…