Related papers: Evidential Confirmation as Transformed Probability
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
Within the framework of evidence theory, the confidence functions of different information can be combined into a combined confidence function to solve uncertain problems. The Dempster combination rule is a classic method of fusing…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…
Probability theory and Dempster-Shafer theory are two germane theories to represent and handle uncertain information. Recent study suggested a transformation to obtain the negation of a probability distribution based on the maximum entropy.…
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…
Causal inference from observational data often assumes "ignorability," that all confounders are observed. This assumption is standard yet untestable. However, many scientific studies involve multiple causes, different variables whose…
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…
Recent progress towards theoretical interpretability guarantees for AI has been made with classifiers that are based on interactive proof systems. A prover selects a certificate from the datapoint and sends it to a verifier who decides the…
Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…
We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility…
Dempster's rule is a fundamental tool for combining belief functions from distinct and reliable sources. However, its intersection-based semantics imposes strong structural restrictions, which limits its flexibility in handling complex…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
We formulate Dempster Shafer Belief functions in terms of Propositional Logic using the implicit notion of provability underlying Dempster Shafer Theory. Given a set of propositional clauses, assigning weights to certain propositional…
The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
By analyzing the relationships among chance, weight of evidence and degree of beliefwe show that the assertion "probability functions are special cases of belief functions" and the assertion "Dempster's rule can be used to combine belief…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…