*A Statistical Model as a Chance Mechanism
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**Aris Spanos**

**Today is the birthday of Jerzy Neyman ****(April 16, 1894 – August 5, 1981).** Neyman was a Polish/American statistician[i] who spent most of his professional career at the University of California, Berkeley. Neyman is best known in statistics for his pioneering contributions in framing the Neyman-Pearson (N-P) optimal theory of hypothesis testing and his theory of Confidence Intervals. (This article was first posted here.)

One of Neyman’s most remarkable, but least recognized, achievements was his adapting of Fisher’s (1922) notion of a statistical model to render it pertinent for non-random samples. Fisher’s original parametric statistical model M_{θ}(**x**) was based on the idea of ‘a hypothetical infinite population’, chosen so as to ensure that the observed data **x**_{0}:=(x_{1},x_{2},…,x_{n}) can be viewed as a ‘truly representative sample’ from that ‘population’:

“The postulate of randomness thus resolves itself into the question, Of what population is this a random sample? (ibid., p. 313), underscoring that: the adequacy of our choice may be tested a posteriori.’’ (p. 314)

In cases where data **x**_{0} come from sample surveys or it can be viewed as a typical realization of a random sample **X**:=(X_{1},X_{2},…,X_{n}), i.e. Independent and Identically Distributed (IID) random variables, the ‘population’ metaphor can be helpful in adding some intuitive appeal to the inductive dimension of statistical inference, because one can imagine using a subset of a population (the sample) to draw inferences pertaining to the whole population. Continue reading