@article {10845,
	title = {Nondimensionalizing physical and statistical models: a unified approach},
	journal = {Statistical Science},
	year = {Submitted},
	pages = {Submitted},
	type = {Research  paper},
	abstract = {<p>This paper presents a version of the statistical invariance principle that incorporates constraints imposed by dimensional analysis. It does so by adapting Buckingham{\textquoteright}s Pi-theorem for deterministic models of physical processes based on vectors of attribute variables, to one for data models for stochastic processes based on random matrices of those attributes. Buckingham{\textquoteright}s method is meant for a priori modeling to reduce the number of attributes, thus simplifying experimental design, and reducing experimental costs.\&nbsp; In contrast, this paper{\textquoteright}s proposal allows for more flexibility in modeling, including a stochasatic component that brings with it a measure of that model{\textquoteright}s uncertainty. The theory is extended to incorporate both a priori and a posteriori Bayesian modeling. A simple example of that extension to regression modelling is given.</p>
},
	author = {Tae Yoon Lee and James V Zidek and Nancy Heckman}
}
