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|a (JST)27643752
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a Gelman, Andrew
|e verfasserin
|4 aut
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|a The Boxer, the Wrestler, and the Coin Flip: A Paradox of Robust Bayesian Inference and Belief Functions
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|c 2006
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
|b c
|2 rdamedia
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|a Online-Ressource
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|a Bayesian inference requires all unknowns to be represented by probability distributions, which awkwardly implies that the probability of an event for which we are completely ignorant (e.g., that the world's greatest boxer would defeat the world's greatest wrestler) must be assigned a particular numerical value such as 1/2, as if it were known as precisely as the probability of a truly random event (e.g., a coin flip). Robust Bayes and belief functions are two methods that have been proposed to distinguish ignorance and randomness. In robust Bayes, a parameter can be restricted to a range, but without a prior distribution, yielding a range of potential posterior inferences. In belief functions (also known as the Dempster-Shafer theory), probability mass can be assigned to subsets of parameter space, so that randomness is represented by the probability distribution and uncertainty is represented by large subsets, within which the model does not attempt to assign probabilities. Through a simple example involving a coin flip and a boxing/wrestling match, we illustrate difficulties with robust Bayes and belief functions. In short: robust Bayes allows ignorance to spread too broadly, and belief functions inappropriately collapse to simple Bayesian models.
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|a Copyright 2006 American Statistical Association
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| 650 |
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4 |
|a Dempster-Shafer theory
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| 650 |
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4 |
|a Epistemic and aleatory uncertainty
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| 650 |
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4 |
|a Foundations of probability
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| 650 |
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|a Ignorance
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| 650 |
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|a Robust Bayes
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| 650 |
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|a Subjective prior distribution
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Probabilities
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| 650 |
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4 |
|a Information science
|x Information management
|x Information classification
|x Cladistics
|x Bayesian inference
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| 650 |
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4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Thought processes
|x Reasoning
|x Inference
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| 650 |
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4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical functions
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Randomness
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| 650 |
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4 |
|a Philosophy
|x Epistemology
|x Uncertainty
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| 650 |
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4 |
|a Philosophy
|x Epistemology
|x Ignorance
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| 650 |
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4 |
|a Philosophy
|x Logic
|x Paradoxes
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
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| 650 |
|
4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Decision making
|x Bayesian theories
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Probabilities
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| 650 |
|
4 |
|a Information science
|x Information management
|x Information classification
|x Cladistics
|x Bayesian inference
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| 650 |
|
4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Thought processes
|x Reasoning
|x Inference
|
| 650 |
|
4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical functions
|
| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Randomness
|
| 650 |
|
4 |
|a Philosophy
|x Epistemology
|x Uncertainty
|
| 650 |
|
4 |
|a Philosophy
|x Epistemology
|x Ignorance
|
| 650 |
|
4 |
|a Philosophy
|x Logic
|x Paradoxes
|
| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
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| 650 |
|
4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Decision making
|x Bayesian theories
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| 655 |
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4 |
|a research-article
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| 773 |
0 |
8 |
|i Enthalten in
|t The American Statistician
|d American Statistical Association, 1947
|g 60(2006), 2, Seite 146-150
|w (DE-627)339869895
|w (DE-600)2064982-4
|x 15372731
|7 nnns
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| 773 |
1 |
8 |
|g volume:60
|g year:2006
|g number:2
|g pages:146-150
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| 856 |
4 |
0 |
|u https://www.jstor.org/stable/27643752
|3 Volltext
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|a AR
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|d 60
|j 2006
|e 2
|h 146-150
|