Related papers: Inclusion within Continuous Belief Functions
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…
We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily…
Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two…
Consistent belief functions represent collections of coherent or non-contradictory pieces of evidence, but most of all they are the counterparts of consistent knowledge bases in belief calculus. The use of consistent transformations cs[.]…
Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention…
Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…
The aim of this paper is to show the interest in fitting features with an $\alpha$-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way…
The conditioning in the Dempster-Shafer Theory of Evidence has been defined (by Shafer \cite{Shafer:90} as combination of a belief function and of an "event" via Dempster rule. On the other hand Shafer \cite{Shafer:90} gives a…
Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…
Belief fusion is the principle of combining separate beliefs or bodies of evidence originating from different sources. Depending on the situation to be modelled, different belief fusion methods can be applied. Cumulative and averaging…
Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictive distributions, respectively, with the latter believed to…
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…
To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of…
The compatibility of quantitative and qualitative representations of beliefs was studied extensively in probability theory. It is only recently that this important topic is considered in the context of belief functions. In this paper, the…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
With the growing popularity of deep-learning based NLP models, comes a need for interpretable systems. But what is interpretability, and what constitutes a high-quality interpretation? In this opinion piece we reflect on the current state…
We present a new approach to dealing with default information based on the theory of belief functions. Our semantic structures, inspired by Adams' epsilon-semantics, are epsilon-belief assignments, where values committed to focal elements…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of…