Frequentist probability

Frequentist probability interprets an event’s probability as the limiting relative frequency with which it occurs across repeated trials under stable conditions.

Relative frequency: The number of times an event occurs divided by the total number of observations or trials. Frequentist probability takes this observed proportion as its empirical starting point.
Bayesian probability: An interpretation of probability as a coherent degree of belief, updated in light of evidence. It assigns probabilities to unique events through belief, not solely through repeatable frequencies.
Maximum likelihood estimation: A method that estimates model parameters by maximizing the likelihood of observed data. Its repeated-sample properties motivate frequentist evaluations of estimator performance.
Reference class problem: The problem of choosing which population or class of cases should determine a probability based on frequencies. Different choices of comparable trials can imply different frequencies for the same event.
Limit (mathematics): A value that a function or sequence approaches as its input or index approaches a specified point. The interpretation identifies probability with a relative frequency’s long-run limit.
Propensity interpretation of probability: An interpretation of probability as a physical disposition of a setup to produce outcomes. It explains chances for individual trials without defining them as long-run frequencies.
Confidence interval: A data-based interval procedure designed to cover a fixed parameter at a specified rate over repeated samples. Its stated coverage is a long-run frequency, not a probability assigned to the fixed parameter.
Single-case probability: The probability assigned to one specific event that has no obvious repeatable class of trials. A unique event challenges an interpretation grounded in repeated outcomes.
Random experiment: A repeatable procedure whose outcome is uncertain before each performance. The interpretation requires a well-defined trial that can be repeated under comparable conditions.
Classical interpretation of probability: An interpretation assigning equal probability to outcomes in a finite set of symmetric possibilities. It derives probabilities from symmetry and counting rather than observed repetition.

Linked from 8 pages