The Foundations of Statistics¶
Savage, L. J. (1954). The Foundations of Statistics. Wiley.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Bayesian Updating
- The prior probability as initial belief state
This sourceEstablishes subjective expected utility: probabilities are an agent's own coherent degrees of belief (priors) rather than objective frequencies. SUPPORTS marker 001 (prior as initial belief state).
- The prior probability as initial belief state
- Belief Formation
- Decision theory: Probability-belief updating, prior selection, expected-utility frameworks that require well-formed beliefs about outcome probabilities, and the construction of subjective probability distributions over uncertain states of the world, a tradition Savage (1954) grounded in his axiomatization of belief and preference in personal probability.
This sourceAxiomatizes subjective expected utility, treating probabilities as the agent's own coherent degrees of belief rather than objective frequencies; (Annotation corrected from a carried-over 'scalar-aggregation' description.)
- Decision theory: Probability-belief updating, prior selection, expected-utility frameworks that require well-formed beliefs about outcome probabilities, and the construction of subjective probability distributions over uncertain states of the world, a tradition Savage (1954) grounded in his axiomatization of belief and preference in personal probability.
- Expected Utility
- Savage (1954) extended the machinery to the subjective case, showing that the probabilities themselves need not be given by nature but can be the agent's own coherent degrees of belief, which broadens the pattern from objective lotteries to any decision under genuine uncertainty.
This sourceEstablishes subjective expected utility: probabilities are the agent's own coherent degrees of belief rather than objective frequencies, extending the pattern to any decision under genuine uncertainty
- Savage (1954) extended the machinery to the subjective case, showing that the probabilities themselves need not be given by nature but can be the agent's own coherent degrees of belief, which broadens the pattern from objective lotteries to any decision under genuine uncertainty.
- Nirvana Fallacy
- A chooser faces a feasible set of options \(\mathcal{A} = \{a_1, \dots, a_n\}\), each with a value \(V(a_i)\), and rational choice is \(\arg\max_{a \in \mathcal{A}} V(a)\) — comparison strictly within \(\mathcal{A}\).
This sourceDevelops the decision-theoretic framework of choosing the act maximizing expected value over a feasible set of options, the formal setting for the argmax-over-the-feasible-set analysis.
- A chooser faces a feasible set of options \(\mathcal{A} = \{a_1, \dots, a_n\}\), each with a value \(V(a_i)\), and rational choice is \(\arg\max_{a \in \mathcal{A}} V(a)\) — comparison strictly within \(\mathcal{A}\).
- Uncertainty
- how the unknowing is represented (a distribution, an interval, a scenario set, a candid "we don't know"), capturing the agent's degree of belief over the unknown's possible values; and (4) the aleatoric-vs-epistemic decomposition
This sourceEstablishes subjective expected utility: probabilities are the agent's own coherent degrees of belief rather than objective frequencies, extending the pattern to any decision under genuine uncertainty; supplies the scalar-aggregation move that renders contingencies directly rankable while remaining silent on the worth of the values or beliefs supplied.
- how the unknowing is represented (a distribution, an interval, a scenario set, a candid "we don't know"), capturing the agent's degree of belief over the unknown's possible values; and (4) the aleatoric-vs-epistemic decomposition
Verification¶
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://search.worldcat.org/title/598698 ×1
- https://www.google.com/books/edition/The_Foundations_of_Statistics/N6CMAwAAQBAJ ×1
Registry ID ref:bc05310c1edd · see in the full table