Dempster-Shafer theory and statistical inference with weak beliefs

DOI10.1214/10-STS322zbMath1328.62040arXiv1011.0819OpenAlexW3106496672MaRDI QIDQ903315

Jianchun Zhang, Chuanhai Liu, Ryan Martin

Publication date: 5 January 2016

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0819

zbMATH Keywords

frequentisthypothesis testingnonparametricsBayesianbelief functionsinferential modelfiducial argument

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Foundations and philosophical topics in statistics (62A01) Knowledge representation (68T30) Reasoning under uncertainty in the context of artificial intelligence (68T37)

Related Items (19)

Prediction of future observations using belief functions: a likelihood-based approach ⋮ Comment on “A Gibbs Sampler for a Class of Random Convex Polytopes,” by Pierre E. Jacob, Ruobin Gong, Paul T. Edlefsen, and Arthur P. Dempster ⋮ Frequency-calibrated belief functions: review and new insights ⋮ New two-sided confidence intervals for binomial inference derived using Walley's imprecise posterior likelihood as a test statistic ⋮ Reweighted and circularised Anderson-Darling tests of goodness-of-fit ⋮ Partial conditioning for inference of many-normal-means with Hölder constraints ⋮ Parameter expansion and efficient inference ⋮ Fiducial theory and optimal inference ⋮ Inference about constrained parameters using the elastic belief method ⋮ A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models ⋮ Inferential Models: A Framework for Prior-Free Posterior Probabilistic Inference ⋮ Random sets and exact confidence regions ⋮ Likelihood-based belief function: justification and some extensions to low-quality data ⋮ Discussion of ``On the Birnbaum argument for the strong likelihood principle ⋮ Uncertainty quantification for honest regression trees ⋮ Large scale two sample multinomial inferences and its applications in genome-wide association studies ⋮ Probabilistic inference for multiple testing ⋮ An IM-based efficient test for non inferiority of the odds ratio between two independent binomial proportions ⋮ Discussion: Foundations of statistical inference, revisited

Cites Work

• Allocations of probability
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• R. A. Fisher and the fiducial argument
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• Estimating limits from Poisson counting data using Dempster-Shafer analysis
• Classic works on the Dempster-Shafer theory of belief functions
• Constructing belief functions from sample data using multinomial confidence regions
• Dempster-Shafer inference with weak beliefs
• The Logic of Inductive Inference
• Upper and Lower Probabilities Induced by a Multivalued Mapping
• New Methods for Reasoning Towards Posterior Distributions Based on Sample Data
• Upper and Lower Probability Inferences for Families of Hypotheses with Monotone Density Ratios
• Further Examples of Inconsistencies in the Fiducial Argument
• A Stochastic Approximation Method
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