Selecting random Latin hypercube dimensions and designs through estimation of maximum absolute pairwise correlation

Latin hypercubes are the most widely used class of design for high-dimensional computer experiments. However, the high correlations that can occur in developing these designs can complicate subsequent analyses. Efforts to reduce or eliminate correlations can be complex and computationally expensive. Consequently, researchers often use uncorrected Latin hypercube designs in their experiments and accept any resulting multicollinearity issues. In this paper, we establish guidelines for selecting the number of runs and/or the number of variables for random Latin hypercube designs that are likely to yield an acceptable degree of correlation. Applying our policies and tools, analysts can generate satisfactory random Latin hypercube designs without the need for complex algorithms.

[1]  T. M. Cioppa,et al.  Efficient nearly orthogonal and space-filling experimental designs for high-dimensional complex models , 2002 .

[2]  Douglas C. Montgomery,et al.  Comparing designs for computer simulation experiments , 2008, 2008 Winter Simulation Conference.

[3]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[4]  M. Morris.  The Design and Analysis of Computer Experiments , 2004 .

[5]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[6]  J. Brian Gray,et al.  Introduction to Linear Regression Analysis , 2002, Technometrics.

[7]  A. Owen.  Controlling correlations in latin hypercube samples , 1994 .

[8]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[9]  Jack P. C. Kleijnen,et al.  State-of-the-Art Review: A User's Guide to the Brave New World of Designing Simulation Experiments , 2005, INFORMS J. Comput..

[10]  John W. Auer,et al.  Linear algebra with applications , 1996 .

[11]  Kenny Q. Ye.  Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments , 1998 .

[12]  Jurusan Statistik.  Advanced Design of Experiments , 2007 .

[13]  V. R. Joseph,et al.  ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS , 2008 .

[14]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[15]  Thomas W. Lucas,et al.  Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes , 2007, Technometrics.

[16]  Alejandro S. Hernandez.  Breaking Barriers to Design Dimensions in Nearly Orthogonal Latin Hypercubes , 2008 .

[17]  Hyunjoong Kim,et al.  Classification Trees With Bivariate Linear Discriminant Node Models , 2003 .

[18]  Douglas C. Montgomery,et al.  Introduction to Linear Regression Analysis, Solutions Manual (Wiley Series in Probability and Statistics) , 2007 .

[19]  Thomas W. Lucas,et al.  Designs for Large‐Scale Simulation Experiments, with Applications to Defense and Homeland Security , 2012 .

[20]  Boxin Tang,et al.  SELECTING LATIN HYPERCUBES USING CORRELATION CRITERIA , 1998 .

[21]  Aleš Florian,et al.  An efficient sampling scheme: Updated Latin Hypercube Sampling , 1992 .

[22]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[23]  H. D. Patterson.  The Errors of Lattice Sampling , 1954 .

[24]  Dennis K. J. Lin,et al.  A construction method for orthogonal Latin hypercube designs , 2006 .