Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 1 Minimum Potential Energy Designs Bradley Jones & Christopher.

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Presentation transcript:

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

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