**By Aris Spanos**

One of R. A. Fisher’s (17 February 1890 — 29 July 1962) most remarkable, but least recognized, achievement was to initiate the recasting of statistical induction. Fisher (1922) pioneered modern frequentist statistics as a model-based approach to statistical induction anchored on the notion of a statistical model, formalized by:

M_{θ}(**x**)={f(**x**;θ); θ∈Θ**}**; **x**∈R^{n };Θ⊂R^{m}; m < n; (1)

where the distribution of the sample f(**x**;θ) ‘encapsulates’ the probabilistic information in the statistical model.

Before Fisher, the notion of a statistical model was vague and often implicit, and its role was primarily conﬁned to the description of the distributional features of the data in hand using the histogram and the ﬁrst few sample moments; implicitly imposing random (IID) samples. The problem was that statisticians at the time would use descriptive summaries of the data to claim generality beyond the data in hand **x**_{0}:=(x_{1},x_{2},…,x_{n}) As late as the 1920s, the problem of statistical induction was understood by Karl Pearson in terms of invoking (i) the ‘stability’ of empirical results for subsequent samples and (ii) a prior distribution for θ.

Fisher was able to recast statistical inference by turning Karl Pearson’s approach, proceeding from data **x**_{0 }in search of a frequency curve f(x;ϑ) to describe its histogram, on its head. He proposed to begin with a prespeciﬁed M_{θ}(**x**) (a ‘hypothetical inﬁnite population’), and view x_{0 }as a ‘typical’ realization thereof; see Spanos (1999). Continue reading