Related papers: The Assumptions Behind Dempster's Rule
Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we…
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…
Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…
It is often reported in forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the "forecast combination puzzle". Motivated…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…
A conceptual foundation for approximation of belief functions is proposed and investigated. It is based on the requirements of consistency and closeness. An optimal approximation is studied. Unfortunately, the computation of the optimal…
In previous articles we presented a simple set of axioms named Contexts, Systems and Modalities (CSM), where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
Statistical methods are based on model assumptions, and it is statistical folklore that a method's model assumptions should be checked before applying it. This can be formally done by running one or more misspecification tests of model…
A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but the…
While Evidence Theory (also known as Dempster-Shafer Theory, or Belief Functions Theory) is being increasingly used in data fusion, its potentialities in the Social and Life Sciences are often obscured by lack of awareness of its…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any…
Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent…
The AGM theory of belief revision has become an important paradigm for investigating rational belief changes. Unfortunately, researchers working in this paradigm have restricted much of their attention to rather simple representations of…
The Principle of Sufficient Reason implies determinism. An explicit indeterministic quantum jump dynamics is constructed, which may be naturally transformed into a deterministic one. A consistent application of the Principle of Sufficient…
Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…