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# Taxonomy 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
``` ____________________________________
|                                    |
|                                    |
|                                    |
|     __________________________     |
|    |                          |    |
|    |                          |    |
|    |      _______________     |    |
|    |     |              |     |    |
|    |     |  Classical   |     |    |
|    |     |______________|     |    |
|    |                          |    |
|    |                          |    |
|    |                          |    |
|    |        Frequency         |    |
|    |__________________________|    |
|                                    |
|                                    |
|                                    |
|             Subjective             |
|____________________________________|

```

## 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.