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Abstract:
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Dimensional Analysis (DA) is a methodology that is widely used in the physical sciences and engineering. The main idea is to extract and deduce key variables based on physical dimensions. Its overlooked importance in statistics has been recognized recently. However, most existing literature treat DA as merely a preprocessing tool, resulting in multiple statistical issues. In particular, those include: (a) the non-unique choice of basis quantities and dimensionless variables; (b) the statistical representation and testing of DA constraints; (c) the spurious correlations between post-DA variables. In this paper, we propose a power law type of "DA conjugate" model that is useful in incorporating dimensional information and analyzing post-DA variables. Adapting the similar idea of "conjugacy" in Bayesian analysis, we show that the proposed modeling technique not only produces flexible and effective results, but also provides good solutions to the above three issues. A modified projection pursuit regression analysis is implemented to fit the proposed models. Two numerical studies are discussed in detail to illustrate and evaluate the advantages of the proposed procedure.
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