The Probable and The Provable

Cohen, L. Jonathan

doi:10.1093/acprof:oso/9780198244127.001.0001

Cited by 724 publications

(255 citation statements)

References 0 publications

Supporting

Mentioning

227

Contrasting

Unclassified

Order By: Relevance

“…From a logical perspective, inductive hypothesis testing and belief update are mostly viewed (but see Cohen, 1977) as a change in the epistemic probability p that a hypothesis H is true (as opposed to false, corresponding to the probability that its complement, ¬H, is true) after acquiring a piece of evidence E, with respect to the probability that H was true before E was acquired. A widespread formal method of belief update is Bayes' rule.…”

Section: Basic Formal Concepts About Hypothesis Testingmentioning

confidence: 99%

Missing the dog that failed to bark in the nighttime: on the overestimation of occurrences over non-occurrences in hypothesis testing

Cherubini

Rusconi

Russo

et al. 2012

Psychological Research

View full text Add to dashboard Cite

In three studies, we investigated whether and to what extent the evaluation of two mutually exclusive hypotheses is affected by a feature-positive effect, wherein present clues are weighted more than absent clues. Participants (N = 126) were presented with abstract problems concerning the most likely provenance of a card that was drawn from one of two decks. We factored the correct response (the hypothesis favored by the consideration of all clues) and the ratio of present-to-absent features in each set of observations. Furthermore, across the studies, we manipulated the presentation format of the features' probabilities by providing the probability distributions of occurrences (Study 1), non-occurrences (Study 3) or both (Study 2). In all studies, both participant preference and accuracy were mostly determined by an over-reliance on present features. Moreover, across participants, both confidence in the responses and the informativeness of the present clues correlated positively with the number of responses given in line with an exclusive consideration of present features. These results were mostly independent of both the rarity of the absent clues and the presentation format. We concluded that the feature-positive effect influences hypothesis evaluation, and we discussed the implications for confirmation bias.

show abstract

Section: Basic Formal Concepts About Hypothesis Testingmentioning

confidence: 99%

Missing the dog that failed to bark in the nighttime: on the overestimation of occurrences over non-occurrences in hypothesis testing

Cherubini

Rusconi

Russo

et al. 2012

Psychological Research

View full text Add to dashboard Cite

show abstract

“…However, degrees of belief cannot always be satisfactorily described with the classical axioms of Kolmogorov, something which has been recognized and confirmed by many researchers from such different disciplines as mathematics [1,[11][12][13]16], legal science [1], and philosophy (see [3,4,6,16] and references therein). These authors have argued that the classical axioms of probability are too restrictive for at least two reasons:…”

Section: P(a ∪ B) = P(a) + P(b) − P(a ∩ B)mentioning

confidence: 99%

A Behavioral Interpretation of Belief Functions

Kerkvliet¹,

Meester²

2017

J Theor Probab

View full text Add to dashboard Cite

Shafer's belief functions were introduced in the seventies of the previous century as a mathematical tool in order to model epistemic probability. One of the reasons that they were not picked up by mainstream probability was the lack of a behavioral interpretation. In this paper, we provide such a behavioral interpretation and re-derive Shafer's belief functions via a betting interpretation reminiscent of the classical Dutch Book Theorem for probability distributions. We relate our betting interpretation of belief functions to the existing literature.

show abstract

“…Independently, the connection between numerical possibility and similarity was investigated by Sudkamp [131]. L. J. Cohen A framework very similar to the one of Shackle was proposed by the philosopher L. J. Cohen [32] who considered the problem of legal reasoning. He introduced socalled Baconian probabilities understood as degrees of provability.…”

Section: Lewismentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

148

101

View full text Add to dashboard Cite

This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. Possibilistic logic provides a rich representation setting, which enables the handling of lower bounds of possibility theory measures, while remaining close to classical logic. Qualitative possibility theory has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

show abstract

The Probable and The Provable

Cited by 724 publications

References 0 publications

Missing the dog that failed to bark in the nighttime: on the overestimation of occurrences over non-occurrences in hypothesis testing

Missing the dog that failed to bark in the nighttime: on the overestimation of occurrences over non-occurrences in hypothesis testing

A Behavioral Interpretation of Belief Functions

Possibility Theory and Its Applications: Where Do We Stand?

Contact Info

Product

Resources

About