Introduction

The frequentist interpretation of probability dominates mainstream probability theory and econometric theory. Proponents of the frequency theory bolster its alleged objectivity, its exclusive reliance on facts. For this reason, it is sometimes called a ‘realistic’ theory (Cohen, 1989).

Keynes ([1921] CW VIII, p. 100) pays tribute to the English mathematician Leslie Ellis, for providing the first logical investigation of the frequency theory of probability. Ellis (1843) objects to relating probability to ignorance: ex nihilo nihil. John Venn ([1866] 1876) elaborated the frequency theory. Still, a theory which is formally satisfactory did not exist until the early twentieth century. In 1919, Richard von Mises formulated the foundations for a frequency theory of probabilistic inference (see von Mises, [1928] 1981, p. 224). His views are discussed in, section 2. Shortly after, Ronald Aylmer Fisher (1922) presented an alternative frequentist foundation of probabilistic inference. Section 3 deals with Fisher's theory. Today, the most popular frequentist theory of probability is based on yet another interpretation, due to Jerzy Neyman and Egon Pearson. This is the topic of, section 4. Popper's interpretation of probability, which is supposed to be entirely ‘objective’, is discussed in section 5. Section 6 offers a summary of the chapter.