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Related papers: A new approach for imprecise probabilities

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Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…

Artificial Intelligence · Computer Science 2013-04-05 Linda C. van der Gaag

Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…

Statistics Theory · Mathematics 2011-04-12 Xinjia Chen

This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…

Artificial Intelligence · Computer Science 2013-03-08 Michael S. K. M. Wong , Z. W. Wang

How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…

Applications · Statistics 2022-11-15 Akisato Suzuki

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…

Statistics Theory · Mathematics 2024-05-27 Marta Catalano , Hugo Lavenant

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

Quantum Physics · Physics 2007-05-23 Johann Summhammer

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…

This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related…

Artificial Intelligence · Computer Science 2013-04-08 Michael Smithson

The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…

Artificial Intelligence · Computer Science 2013-04-15 Norman C. Dalkey

In this paper we discuss the consistency concept of Williams coherence for imprecise conditional previsions, presenting a variant of this notion, which we call W-coherence. It is shown that W-coherence ensures important consistency…

Probability · Mathematics 2015-03-10 Renato Pelessoni , Paolo Vicig

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

Quantum Physics · Physics 2018-11-30 Yanbao Zhang , Emanuel Knill , Peter Bierhorst

Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to random phenomena that exhibit diverging relative…

Statistics Theory · Mathematics 2023-06-07 Christian Fröhlich , Rabanus Derr , Robert C. Williamson

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

Artificial Intelligence · Computer Science 2013-03-26 Arthur Ramer

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

Methodology · Statistics 2021-10-26 Dimitris G. Giovanis , Michael Shields

One of the most popular methods of the machine learning prediction explanation is the SHapley Additive exPlanations method (SHAP). An imprecise SHAP as a modification of the original SHAP is proposed for cases when the class probability…

Machine Learning · Computer Science 2021-06-18 Lev V. Utkin , Andrei V. Konstantinov , Kirill A. Vishniakov

Evidence theory is that the extension of probability can better deal with unknowns and inaccurate information. Uncertainty measurement plays a vital role in both evidence theory and probability theory. Approximate Entropy (ApEn) is proposed…

Artificial Intelligence · Computer Science 2021-05-19 Tianxiang Zhan , Yuanpeng He , Hanwen Li , Fuyuan Xiao

Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…

Artificial Intelligence · Computer Science 2011-02-02 Ping Zhu , Qiaoyan Wen

In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…

Artificial Intelligence · Computer Science 2012-10-19 Giuseppe Sanfilippo