Posts Tagged With: all models are wrong

Lifting a piece from Spanos’ contribution* will usefully add to the mix

The following two sections from Aris Spanos’ contribution to the RMM volume are relevant to the points raised by Gelman (as regards what I am calling the “two slogans”)**.

 6.1 Objectivity in Inference (From Spanos, RMM 2011, pp. 166-7)

The traditional literature seems to suggest that ‘objectivity’ stems from the mere fact that one assumes a statistical model (a likelihood function), enabling one to accommodate highly complex models. Worse, in Bayesian modeling it is often misleadingly claimed that as long as a prior is determined by the assumed statistical model—the so called reference prior—the resulting inference procedures are objective, or at least as objective as the traditional frequentist procedures:

“Any statistical analysis contains a fair number of subjective elements; these include (among others) the data selected, the model assumptions, and the choice of the quantities of interest. Reference analysis may be argued to provide an ‘objective’ Bayesian solution to statistical inference in just the same sense that conventional statistical methods claim to be ‘objective’: in that the solutions only depend on model assumptions and observed data.” (Bernardo 2010, 117)

This claim brings out the unfathomable gap between the notion of ‘objectivity’ as understood in Bayesian statistics, and the error statistical viewpoint. As argued above, there is nothing ‘subjective’ about the choice of the statistical model Mθ(z) because it is chosen with a view to account for the statistical regularities in data z0, and its validity can be objectively assessed using trenchant M-S testing. Model validation, as understood in error statistics, plays a pivotal role in providing an ‘objective scrutiny’ of the reliability of the ensuing inductive procedures.

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Categories: Philosophy of Statistics, Statistics, Testing Assumptions, U-Phil | Tags: , , , , | 43 Comments

If you try sometime, you find you get what you need!

picking up the pieces
Thanks to Nancy Cartwright, a little ad hoc discussion group has formed: “PhilErrorStat: LSE: Three weeks in (Nov-Dec) 2011.”  I’ll be posting related items on this blog, in the column to your left, over its short lifetime. We’re taking a look at some articles and issues leading up to a paper I’m putting together to give in Madrid next month on the Birnbaum-likelihood principle business (“Breaking Through the Breakthrough”) at a conference (“The Controversy about Hypothesis Testing,” Madrid, December 15-16, 2011).  I hope also to get this group’s feedback as I follow through on responses I’ve been promising to some of the comments and queries I’ve received these past few months. Continue reading
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