Introduction

What can we infer about a universe from a given sample? This is the recurring question of probabilistic inference. Bowley ([1901] 1937, p. 409), answers that the only bridge is the Bayesian one. In a footnote, he makes the distinction between the problem ‘given the target how will shots be dispersed?’ and ‘given the shot-marks, what was the target?’ The first question can be answered by means of Fisher's analysis of variance, the second ‘is the practical question in many cases when we have only one sample’ and necessarily depends on Bayesian inference (p. 409).

But the Bayesian argument never gained a strong foothold in econometrics: the frequency theory prevailed. The link between probability theory and practical statistics is sampling theory, which should provide the justification for using (parametric) regression techniques of inference. But econometrics uses sampling theory more in a rhetorical than in the real sense. This chapter discusses the limitations of sampling theory in econometrics.

This chapter deals with how the different elements of probability filtered into econometrics. Section 2 briefly reconsiders the key elements of sampling theory. Section 3 is about regression. The contributions of Galton and Yule are discussed, including Galton's fallacy and ‘nonsense correlation’.