Concepts of probability
Probability is not a thing – it is many concepts. All concepts obey the same fundamental rules, but the concept employed in a specific analysis determines the manner in which probably is introduced to the problem, and the interpretation of inferential statements. Difference concepts lead to different approaches to developing an analysis
Laplacian probability
(aka, Classical, gambling probability)
Elements of the sample space (basic outcomes) are equally likely. `P(E) = (|E|) / (|S|)`. Fundamental characteristic of equally likely outcomes usually result of physical properties of operation.
Limited, but used more often that you might think. Used directly in some randomisation procedures.
Relative frequency probability
- Finite number of physically existing objects in a class `B`
- An operation consists of observing whether a selected object also belongs
- to class `A`.
- `P(A | B) = (|A|) / (|B|)`
Probability is a direct consequence of physical realities (ie. things that actually happened). Clearly inadequate, but can apply in problems that involve finite populations.
Hypothetical limiting relative frequency probability
- Operations that can (at least hypothetically) be repeated an infinite
- number of times
- Sample space
- Events
Epistemic probability
- Probability = knowledge or belief
- Belief updated in light of observed information
- Mathmatical formalism necessary so that belief modifed in coherent manner