Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 1 Minimum Potential Energy Designs Bradley Jones & Christopher Gotwalt SAS Institute Inc. Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 2 Abstract Introducing a new class of space filling designs based on a physical analogy of design points as protons connected by springs. Properties Spherical symmetry Nearly orthogonal Uniform Spacing Easy to compute with unconstrained optimization code Outline Show how to generate these designs Discuss their properties Give examples with different numbers of factors & sample sizes Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 3 Illustration of Core Idea Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 4 Objective function where d ij is the distance between the ith and jth points. Goal: Find the design that minimizes the above function Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 5 Spherical Symmetry Uniform Spacing Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 6 Near Orthogonal 12 Factor 24 Run Design Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 7 Estimation Efficiency for Low Order Polynomial Models FactorsRunsD-Efficiency % % D-Efficiency for full quadratic model. Four and five factor designs have an added center point. Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 8 Two Factor Designs Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 9 4 points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS Points Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 29 Three Factors Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 30 Four Factors Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 31 Conclusions Benefits Spherical symmetry Nearly orthogonal Uniform Spacing Available in commercial software Negative Not space filling in higher dimensions (except in low dimensional projections. Copyright 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 32 Contact Information