Related papers: Is Shafer General Bayes?
Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to…
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…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
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…
An established and growing literature on generalized fiducial inference and related fiducial ideas points to the adoption of fiducial inference as a mainstream perspective among modern statisticians. Like Bayesian posteriors, generalized…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea 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…
Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…
How to manage conflict is still an open issue in Dempster-Shafer evidence theory. The correlation coefficient can be used to measure the similarity of evidence in Dempster-Shafer evidence theory. However, existing correlation coefficients…
In the current versions of the Dempster-Shafer theory, the only essential restriction on the validity of the rule of combination is that the sources of evidence must be statistically independent. Under this assumption, it is permissible to…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…
The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particular not on the choice of a data generating model. The…
Dempster-Shafer Theory (DST) provides a powerful framework for modeling uncertainty and has been widely applied to multi-attribute classification tasks. However, traditional DST-based attribute fusion-based classifiers suffer from…
Multi-sensor data fusion technology plays an important role in real applications. Because of the flexibility and effectiveness in modelling and processing the uncertain information regardless of prior probabilities, Dempster-Shafer evidence…
One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of belief functions from data. In probability theory…
As a generalization of Dempster-Shafer theory, D number theory provides a framework to deal with uncertain information with non-exclusiveness and incompleteness. However, some basic concepts in D number theory are not well defined. In this…
Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…
Dempster-Shafer evidence theory is an efficient mathematical tool to deal with uncertain information. In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty. Decision-making…
In this paper, we describe a scheme for propagating belief functions in certain kinds of trees using only local computations. This scheme generalizes the computational scheme proposed by Shafer and Logan1 for diagnostic trees of the type…