Frequentist Probability

The primary objective of this article is to discuss a model-based frequentist interpretation that identifies the probability of an event with the limit of its relative frequency of occurrence. What differentiates the proposed interpretation from the traditional ones are several key features: (i) events and probabilities are defined in the context of a statistical model , (ii) it is anchored on the strong law of large numbers, (iii) it is justified on empirical grounds by validating the model assumptions vis-à-vis data , (iv) the “long-run” metaphor can be rendered operational by simple simulation based on , and (v) the link between probability and real-world phenomena is provided by viewing data as a “truly typical” realization of the stochastic mechanism defined by . This link constitutes a feature shared with the Kolmogorov complexity algorithmic perspective on probability, which provides a further justification for the proposed frequentist interpretation.