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# Taxonomy of Probability

## Interpretations of Probability

## Hierarchy of generality

- Classical theory is restricted to equipossible cases
- Frequency theory is restricted to repeatable, random phenomena
- Subjectiveist theory applies to an event about which the agent is uncertain

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## Taxonomy

Classical
(Laplace)
Frequency
(von Mises)
Propensity
(Popper)
Bayesian
/ \
/ \
/ \
/ \
objective subjective
/ \ (Ramsey, de Finetti)
/ \
/ \
/ \
/ \
/ \
logical empirical
(Carnap, Jaynes) (Reichenbach)
Mathematical
(Kolmogorov)

## Notes

- Mathematical probability is distinct from the other five varieties which are "real world" probabilities.
- The vast majority of statisticians are frequentists rather than Bayesians.
- Frequentists are increasingly seeing the light and coming out as Bayesians.
- Most Bayesians are subjective.
- Good (1971) identified 46656 varieties of Bayesians.