Frequentist probability
a.k.a: frequentism, long run probability
An interpretation of probability as the limit of its relative frequency in many trials (the long run probability)
- discussed only when dealing with well-defined random experiments:
- sample space: the set of all possible outcomes of a random experiment,
- an event: a particular subset of the sample space to be considered
- for any given event, only 1 of 2 possibilities may hold: occurs or not occurs.
- probabilities can be found (in principle) by a repeatable objective process
- measured by the relative frequency of occurrence of an event, observed in a number of repetitions of the experiment.
- why many trials ?
- to devoid opinion (ideally)
Motivation
Motivated by the problems and paradoxes of the previous dominant viewpoint, the
classical probability
What
An interpretation of probability where probability is defined
- in terms of principle of difference
- based on the natural symmetry of a problem
- e.g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube.
This classical interpretation stumbled at any statistical problem that has no natural symmetry for reasoning.
Link to original
Properties
- Entails a view that probability is nonsensical in the absence of pre-existing data.
- A claim of the frequentist approach is that, as the number of trials increases, the change in the relative frequency will diminish. → one can view a probability as the limiting value of the corresponding relative frequencies.
- It offers distinct guidance for how to apply mathematical probability theory to the construction and design of practical experiments, especially when contrasted with the Bayesian interpretation.
- As to whether this guidance is useful, or is apt to mis-interpretation, has been a source of controversy.
Frequentist inference
- A type of statistical inference
- Based on Frequentist probability
- treats probability in equivalent terms as frequency
- draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data.
Examples
- p-value
- confidence interval
- null hypothesis significance testing