Dimensional Analysis, Statistical Modelling and the Unconscious Statistician
Date & Time
Thursday, May 5, 2022, 12:00 PM - 12:40 PM
Jim Zidek

Physical scientists have long recognized that units of measurement, scales, and dimensions are fundamental to a physical model like e.g. Newton's second law F = ma. But since at least as far back as the famous work of Buckingham and Bridgman near the beginning of the last century, the legitimacy of such models was also seen to require that they be non-dimensionalizable: they cannot ultimately depend on how the statistician chooses to measurement the quantities involved. Hence, that those models must be non-dimensionalizable. For example in terms of what Buckingham calls a pi-function, Newton's law can be expressed as pi = F/(ma) = 1 no matter how the F, m and a are measured as long as the units are dimensionally consistent. This principle has also been embraced in statistical science in its invariance principle. As Jim Berger says in his well-known book on decision theory and Bayesian analysis: "...the action taken should not depend on the unit of measurement.” Despite the apparent similarity in the aspirations behind the physical and statistical modelling paradigms, no attempt has been made until recently to unify them for mutual benefit. Worse still, statisticians seldom even mention units in disseminating their work, nor do they exploit the simplifications in modelling that can be achieved through the imposition of dimensional consistency. Such benefit will be illustrated in multivariate regression analysis, after extending the invariance principle to cover the Bayesian paradigm. At the same time, in this fairly expository presentation, we will show how physical modellers can benefit by recognizing that through the Bayesian paradigm, model uncertainty can be characterized by applying that paradigm

Session Link