Selecting an Informative/Discriminating Multivariate Response for Inverse Prediction

Abstract

Inverse prediction is important in a variety of scientific and engineering applications, such as to predict properties/characteristics of an object by using multiple measurements obtained from it. Inverse prediction can be accomplished by inverting parameterized forward models that relate the measurements (responses) to the properties/characteristics of interest. Sometimes forward models are computational/science based; but often, forward models are empirically based response surface models, obtained by using the results of controlled experimentation. For empirical models, it is important that the experiments provide a sound basis to develop accurate forward models in terms of the properties/characteristics (factors). While nature dictates the causal relationships between factors and responses, experimenters can control the complexity, accuracy, and precision of forward models constructed via selection of factors, factor levels, and the set of trials that are performed. Recognition of the uncertainty in the estimated forward models leads to an errors-in-variables approach for inverse prediction. The forward models (estimated by experiments or science based) can also be used to analyze how well candidate responses complement one another for inverse prediction over the range of the factor space of interest. One may find that some responses are complementary, redundant, or noninformative. Simple analysis and examples illustrate how an informative and discriminating subset of responses could be selected among candidates in cases where the number of responses that can be acquired during inverse prediction is limited by difficulty, expense, and/or availability of material.

• Calibration
• Errors in Variables
• Glass Composition
• Nuclear Forensics
• Total Least Squares

Additional information

Notes on contributors

Edward V. Thomas

Dr. Thomas is a Statistician who recently retired from Sandia National Laboratories. His email is [email protected].

John R. Lewis

Dr. Lewis is a Statistician in the Statistical Sciences Department. His email is [email protected].

Christine M. Anderson-Cook

Dr. Anderson-Cook is a Research Scientist in the Statistical Sciences Group. She is a Fellow of ASQ. Her email is [email protected].

Tom Burr

Dr. Burr is a Statistician in the Statistical Sciences Group. His email is [email protected].

Michael S. Hamada

Dr. Hamada is a Scientist in the Statistical Sciences Group. He is a Fellow of ASQ. His email is [email protected].