Scope
The frequentist interpretation is a philosophical approach to the definition and use of probabilities; it is one of several, and, historically, the earliest to challenge the classical interpretation. It does not claim to capture all connotations of the concept 'probable' in colloquial speech of natural languages.
As an interpretation, it is not in conflict with the mathematical axiomatization of probability theory; rather, it provides guidance for how to apply mathematical probability theory to real-world situations. It offers distinct guidance in 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. Particularly when the frequency interpretation of probability is mistakenly assumed to be the only possible basis for frequentist inference. So, for example, a list of mis-interpretations of the meaning of p-values accompanies the article on p-values; controversies are detailed in the article on statistical hypothesis testing. The Jeffreys–Lindley paradox shows how different interpretations, applied to the same data set, can lead to different conclusions about the 'statistical significance' of a result.
As William Feller noted:
There is no place in our system for speculations concerning the probability that the sun will rise tomorrow. Before speaking of it we should have to agree on an (idealized) model which would presumably run along the lines "out of infinitely many worlds one is selected at random..." Little imagination is required to construct such a model, but it appears both uninteresting and meaningless.Read more about this topic: Frequentist Probability
Famous quotes containing the word scope:
“For it is not the bare words but the scope of the writer that gives the true light, by which any writing is to be interpreted; and they that insist upon single texts, without considering the main design, can derive no thing from them clearly.”
—Thomas Hobbes (1579–1688)
“A country survives its legislation. That truth should not comfort the conservative nor depress the radical. For it means that public policy can enlarge its scope and increase its audacity, can try big experiments without trembling too much over the result. This nation could enter upon the most radical experiments and could afford to fail in them.”
—Walter Lippmann (1889–1974)
“Happy is that mother whose ability to help her children continues on from babyhood and manhood into maturity. Blessed is the son who need not leave his mother at the threshold of the world’s activities, but may always and everywhere have her blessing and her help. Thrice blessed are the son and the mother between whom there exists an association not only physical and affectional, but spiritual and intellectual, and broad and wise as is the scope of each being.”
—Lydia Hoyt Farmer (1842–1903)