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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 on theme: "Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 1 Minimum Potential Energy Designs Bradley Jones & Christopher."— Presentation transcript:

1 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.

2 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

3 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 3 Illustration of Core Idea

4 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

5 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 5 Spherical Symmetry – Uniform Spacing

6 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 6 Near Orthogonal 12 Factor 24 Run Design

7 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 7 Estimation Efficiency for Low Order Polynomial Models FactorsRunsD-Efficiency 26-8100% 31198.5% 41598.6 52199.3 D-Efficiency for full quadratic model. Four and five factor designs have an added center point.

8 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 8 Two Factor Designs

9 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 9 4 points

10 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 10 5 points

11 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 11 6 points

12 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 12 7 points

13 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 13 8 points

14 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 14 9 points

15 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 15 10 points

16 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 16 11 points

17 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 17 12 points

18 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 18 13 points

19 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 19 14 points

20 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 20 15 points

21 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 21 16 Points

22 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 22 17 Points

23 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 23 18 Points

24 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 24 19 Points

25 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 25 20 Points

26 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 26 50 points

27 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 27 96 Points

28 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 28 200 Points

29 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 29 Three Factors

30 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 30 Four Factors

31 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.

32 Copyright © 2005, SAS Institute Inc. All rights reserved. Statistical Discovery. TM From SAS. 32 Contact Information Bradley.Jones@jmp.com

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