# Posts Tagged With: Models/Modelling

## Guest Blog: ARIS SPANOS: The Enduring Legacy of R. A. Fisher 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:

Mθ(x)={f(x;θ); θ∈Θ}; x∈Rn ;Θ⊂Rm; 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 x0:=(x1,x2,…,xn) 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 x0 in search of a frequency curve f(x;ϑ) to describe its histogram, on its head. He proposed to begin with a prespeciﬁed Mθ(x) (a ‘hypothetical inﬁnite population’), and view x0 as a ‘typical’ realization thereof; see Spanos (1999). Continue reading

## Aris Spanos: The Enduring Legacy of R. A. Fisher More Fisher insights from A. Spanos, this from 2 years ago:

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:

Mθ(x)={f(x;θ); θ∈Θ}; x∈Rn ;Θ⊂Rm; 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 x0:=(x1,x2,…,xn). 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 x0 in search of a frequency curve f(x;ϑ) to describe its histogram, on its head. He proposed to begin with a prespeciﬁed Mθ(x) (a ‘hypothetical inﬁnite population’), and view x0 as a ‘typical’ realization thereof; see Spanos (1999).

In my mind, Fisher’s most enduring contribution is his devising a general way to ‘operationalize’ errors by embedding the material ex­periment into Mθ(x), and taming errors via probabiliﬁcation, i.e. to deﬁne frequentist error probabilities in the context of a statistical model. These error probabilities are (a) deductively derived from the statistical model, and (b) provide a measure of the ‘eﬀectiviness’ of the inference procedure: how often a certain method will give rise to correct in­ferences concerning the underlying ‘true’ Data Generating Mechanism (DGM). This cast aside the need for a prior. Both of these key elements, the statistical model and the error probabilities, have been reﬁned and extended by Mayo’s error statistical approach (EGEK 1996). Learning from data is achieved when an inference is reached by an inductive procedure which, with high probability, will yield true conclusions from valid inductive premises (a statistical model); Mayo and Spanos (2011). Continue reading

Categories: Fisher, phil/history of stat, Statistics | | 2 Comments

## Guest Blogger. ARIS SPANOS: The Enduring Legacy of R. A. Fisher 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:

Mθ(x)={f(x;θ); θ∈Θ}; x∈Rn ;Θ⊂Rm; 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 x0:=(x1,x2,…,xn) 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.

Categories: Statistics | | 5 Comments

## RMM-4: Special Volume on Stat Scie Meets Phil Sci

The article “Foundational Issues in Statistical Modeling: Statistical Model Specification and Validation*” by Aris Spanos has now been published in our special volume of the on-line journal, Rationality, Markets, and Morals (Special Topic: Statistical Science and Philosophy of Science: Where Do/Should They Meet?”)