Bayesian
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A Bayesian is a statistician who starts with a prior belief then transitions to a posterior belief based on new information and Bayes' rule.
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- Example(s):
- Counter-Example(s):
- See: Bayesian Probability, Bayesian Inference.
References
2016
- http://m-phi.blogspot.com/2017/01/the-principal-principle-does-not-imply.html
- QUOTE: All Bayesian epistemologists agree on two claims. The first, which we might call Precise Credences, says that an agent's doxastic state at a given time t in her epistemic life can be represented by a single credence function Pt, which assigns to each proposition A about which she has an opinion a precise numerical value Pt(A) that is at least 0 and at most 1. Pt(A) is the agent's credence in A at t. It measures how strongly she believes A at t, or how confident she is at t that A is true. The second point of agreement, which is typically known as Probabilism, says that an agent's credence function at a given time should be a probability function: that is, for all times t, Pt(⊤)=1 for any tautology ⊤, Pt(⊥)=0 for any contradiction ⊥, and Pt(A∨B)=Pt(A)+Pt(B)−Pt(AB) for any propositions A and B.
So Precise Credences and Probabilism form the core of Bayesian epistemology. But, beyond these two norms, there is little agreement between its adherents.
- QUOTE: All Bayesian epistemologists agree on two claims. The first, which we might call Precise Credences, says that an agent's doxastic state at a given time t in her epistemic life can be represented by a single credence function Pt, which assigns to each proposition A about which she has an opinion a precise numerical value Pt(A) that is at least 0 and at most 1. Pt(A) is the agent's credence in A at t. It measures how strongly she believes A at t, or how confident she is at t that A is true. The second point of agreement, which is typically known as Probabilism, says that an agent's credence function at a given time should be a probability function: that is, for all times t, Pt(⊤)=1 for any tautology ⊤, Pt(⊥)=0 for any contradiction ⊥, and Pt(A∨B)=Pt(A)+Pt(B)−Pt(AB) for any propositions A and B.
2007
- (Branden, 2007) ⇒ Branden Fitelson. (2007). “Likelihoodism, Bayesianism, and Relational Confirmation.” In: Synthese, 156(3). doi:10.1007/s11229-006-9134-9
- ABSTRACT: Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation).
2003
- (Korb & Nicholson, 2003) ⇒ Kevin B. Korb, and Ann E. Nicholson. (2003). “Bayesian Artificial Intelligence." Chapman & Hall/CRC.
- QUOTE: Bayesianism is the philosophy that asserts that in order to understand human opinions as it ought to be, constrained by ignorance and uncertainty, the probability calculus is the single most important tool for representing appropriate strengths of belief. … It is commonly taken as axiomatic by Bayesians that agents ought to maximize their expected utility.
1991
- (Tanner, 1991) ⇒ Martin A. Tanner. (1991). “Methods for the Exploration of Posterior Distributions and Likelihood Functions" In: "Tools for statistical inference." ISBN:978-1-4684-0194-3
- QUOTE: … The frequentist, in contrast to the Bayesians or to the likelihoodists (ie those who do base … at the mode are of great value to the frequentist's large sample (normal-based) inference approach … Thus, while to the Bayesian or to the likelihoodist tools such as data augmentation, Gibbs …
1954
- (Savage, 1954) ⇒ L.J. Savage. (1954). “The Foundations of Statistics." New York: John Wiley & Sons, Inc. ISBN 0-486-62349-1.
1950
- (Carnap, 1950) ⇒ Rudolph Carnap. (1950). “Logical Foundations of Probability." University of Chicago Press.
- NOTES: Carnap coined the notion "probability1" and "probability2" for evidential and physical probability, respectively.
1937
- (de Finetti, 1937) ⇒ Bruno de Finetti. (1964). “Foresight: its Logical laws, its Subjective Sources". In Kyburg, H. E. Studies in Subjective Probability. H. E. Smokler. New York: Wiley.
- NOTES: Translation of the 1937 French original with later notes added.