Skip to main content

Space-Filling Designs for Computer Experiments

  • Chapter
  • First Online:
The Design and Analysis of Computer Experiments

Part of the book series: Springer Series in Statistics ((SSS))

Abstract

This chapter and the next discuss how to select inputs at which to compute the output of a computer experiment to achieve specific goals. The inputs one selects constitute the “experimental design.” As in previous chapters, the inputs are referred to as “runs.” The region corresponding to the values of the inputs that is to be studied is called the experimental region. A point in this region corresponds to a specific set of values of the inputs. Thus, an experimental design is a specification of points (runs) in the experimental region at which the response is to be computed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Atkinson AC, Donev AN (1992) Optimum experimental designs. Clarendon Press, Oxford

    MATH  Google Scholar 

  • Ba S, Joseph VR (2011) Multi-layer designs for computer experiments. J Am Stat Assoc 106:1139–1149

    Article  MathSciNet  Google Scholar 

  • Ba S, Myers WR, Brenneman WA (2015) Optimal sliced Latin hypercube designs. Technometrics 57(4):479–487

    Article  MathSciNet  Google Scholar 

  • Bates RA, Buck RJ, Riccomagno E, Wynn HP (1996) Experimental design and observation for large systems. J R Stat Soc Ser B 58:77–94

    MathSciNet  MATH  Google Scholar 

  • Bernardo MC, Buck RJ, Liu L, Nazaret WA, Sacks J, Welch WJ (1992) Integrated circuit design optimization using a sequential strategy. IEEE Trans Comput Aided Des 11:361–372

    Article  Google Scholar 

  • Box GE, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New York, NY

    MATH  Google Scholar 

  • Box G, Hunter W, Hunter J (1978) Statistics for experimenters. Wiley, New York, NY

    MATH  Google Scholar 

  • Bratley P, Fox BL, Niederreiter H (1994) Algorithm 738: programs to generate Niederreiter’s low-discrepancy sequences. ACM Trans Math Softw 20:494–495

    Article  Google Scholar 

  • Butler NA (2001) Optimal and orthogonal Latin hypercube designs for computer experiments. Biometrika 88:847–857

    Article  MathSciNet  Google Scholar 

  • Chapman WL, Welch WJ, Bowman KP, Sacks J, Walsh JE (1994) Arctic sea ice variability: model sensitivities and a multidecadal simulation. J Geophys Res 99(C1):919–935

    Article  Google Scholar 

  • Chen RB, Wang W, Wu CFJ (2011) Building surrogates with overcomplete bases in computer experiments with applications to bistable laser diodes. IEE Trans 182:978–988

    Google Scholar 

  • Cioppa TM, Lucas TW (2007) Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49:45–55

    Article  MathSciNet  Google Scholar 

  • Craig PC, Goldstein M, Rougier JC, Seheult AH (2001) Bayesian forecasting for complex systems using computer simulators. J Am Stat Assoc 96:717–729

    Article  MathSciNet  Google Scholar 

  • Dean AM, Voss D, Draguljic D (2017) Design and analysis of experiments, 2nd edn. Springer, New York, NY

    Book  Google Scholar 

  • Dette H, Pepelyshev A (2010) Generalized Latin hypercube designs for computer experiments. Technometrics 52:421–429

    Article  MathSciNet  Google Scholar 

  • Draguljić D, Santner TJ, Dean AM (2012) Non-collapsing spacing-filling designs for bounded polygonal regions. Technometrics 54:169–178

    Article  MathSciNet  Google Scholar 

  • Fang KT, Lin DKJ, Winker P, Zhang Y (2000) Uniform design: theory and application. Technometrics 42:237–248

    Article  MathSciNet  Google Scholar 

  • Fang KT, Li R, Sudjianto A (2006) Design and modeling for computer experiments. Chapman & Hall/CRC, Boca Raton, FL

    Google Scholar 

  • Halton JH (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer Math 2(1):84–90

    Article  MathSciNet  Google Scholar 

  • Handcock MS (1991) On cascading Latin hypercube designs and additive models for experiments. Commun Stat Theory Methods 20(2):417–439

    Article  MathSciNet  Google Scholar 

  • Hayeck GT (2009) The kinematics of the upper extremity and subsequent effects on joint loading and surgical treatment. PhD thesis, Cornell University, Ithaca, NY

    Google Scholar 

  • Hedayat A, Sloane N, Stufken J (1999) Orthogonal arrays. Springer, New York, NY

    Book  Google Scholar 

  • Hickernell FJ (1998) A generalized discrepancy and quadrature error bound. Math Comput 67:299–322

    Article  MathSciNet  Google Scholar 

  • John JA (1987) Cyclic designs. Chapman & Hall, New York, NY

    Book  Google Scholar 

  • John PWM (1980) Incomplete block designs. M. Dekker, Inc., New York, NY

    MATH  Google Scholar 

  • Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plann Inf 26:131–148

    Article  MathSciNet  Google Scholar 

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492

    Article  MathSciNet  Google Scholar 

  • Joseph VR, Gul E, Ba S (2015) Maximum projection designs for computer experiments. Biometrika 102(2):371–380

    Article  MathSciNet  Google Scholar 

  • Kennedy MC, O’Hagan A (2000) Predicting the output from a complex computer code when fast approximations are available. Biometrika 87:1–13

    Article  MathSciNet  Google Scholar 

  • Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models (with discussion). J R Stat Soc Ser B 63:425–464

    Article  MathSciNet  Google Scholar 

  • Liefvendahl M, Stocki R (2006) A study on algorithms for optimization of Latin hypercubes. J Stat Plann Inf 136:3231–3247

    Article  MathSciNet  Google Scholar 

  • Loeppky JL, Sacks J, Welch WJ (2009) Choosing the sample size of a computer experiment: a practical guide. Technometrics 51(4):366–376

    Article  MathSciNet  Google Scholar 

  • Loeppky JL, Moore LM, Williams BJ (2012) Projection array based designs for computer experiments. J Stat Plann Inf 142:1493–1505

    Article  MathSciNet  Google Scholar 

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245

    MathSciNet  MATH  Google Scholar 

  • Mease D, Bingham D (2006) Latin hyperrectangle sampling for computer experiments. Technometrics 48:467–477

    Article  MathSciNet  Google Scholar 

  • Morris MD, Mitchell TJ (1995) Exploratory designs for computational experiments. J Stat Plann Inf 43:381–402

    Article  Google Scholar 

  • Niederreiter H (1988) Low-discrepancy and low-dispersion sequences. J Number Theory 30:51–70

    Article  MathSciNet  Google Scholar 

  • Niederreiter H (1992) Random number generation and quasi-Monte Carlo methods. SIAM, Philadelphia, PA

    Book  Google Scholar 

  • Owen AB (1992a) A central limit theorem for Latin hypercube sampling. J R Stat Soc Ser B Methodol 54:541–551

    MathSciNet  MATH  Google Scholar 

  • Owen AB (1992b) Orthogonal arrays for computer experiments, integration and visualization. Stat Sinica 2:439–452

    MathSciNet  MATH  Google Scholar 

  • Owen AB (1995) Randomly permuted (t, m, s)-nets and (t, s) sequences. In: Niederreiter H, Shiue PJS (eds) Monte Carlo and quasi-Monte Carlo methods in scientific computing. Springer, New York, NY, pp 299–317

    Chapter  Google Scholar 

  • Park JS (1994) Optimal Latin-hypercube designs for computer experiments. J Stat Plann Inf 39:95–111

    Article  MathSciNet  Google Scholar 

  • Pukelsheim F (1993) Optimal design of experiments. Wiley, New York, NY

    MATH  Google Scholar 

  • Qian PZ, Seepersad CC, Joseph VR, Allen JK, Wu CFJ (2006) Building surrogate models with details and approximate simulations. ASME J Mech Des 128:668–677

    Article  Google Scholar 

  • Qian PZG (2009) Nested Latin hypercube designs. Biometrika 96:957–970

    Article  MathSciNet  Google Scholar 

  • Qian PZG (2012) Sliced Latin hypercube designs. J Am Stat Assoc 107:393–399

    Article  MathSciNet  Google Scholar 

  • Qian PZG, Wu CFJ (2008) Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments. Technometrics 50(2):192–204

    Article  MathSciNet  Google Scholar 

  • Raghavarao D (1971) Constructions and combinatorial problems in design of experiments. Wiley, New York, NY

    MATH  Google Scholar 

  • Silvey SD (1980) Optimal design: an introduction to the theory for parameter estimation. Chapman & Hall, New York, NY

    Book  Google Scholar 

  • Sobol´ IM (1967) On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput Math Math Phys 7(4):86–112

    Article  MathSciNet  Google Scholar 

  • Sobol´ IM (1976) Uniformly distributed sequences with an additional uniform property. USSR Comput Math Math Phys 16(5):236–242

    Article  Google Scholar 

  • Stein ML (1987) Large sample properties of simulations using Latin hypercube sampling. Technometrics 29:143–151

    Article  MathSciNet  Google Scholar 

  • Stinstra E, den Hertog D, Stehouwer P, Vestjens A (2003) Constrained maximin designs for computer experiments. Technometrics 45(4):340–346

    Article  MathSciNet  Google Scholar 

  • Street AP, Street DJ (1987) Combinatorics of experimental design. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Tan MHY (2013) Minimax designs for finite design regions. Technometrics 55:346–358

    Article  MathSciNet  Google Scholar 

  • Tang B (1993) Orthogonal array-based Latin hypercubes. J Am Stat Assoc 88:1392–1397

    Article  MathSciNet  Google Scholar 

  • Trosset MW (1999) Approximate maximin distance designs. In: ASA Proceedings of the section on physical and engineering sciences. American Statistical Association, Alexandria, VA, pp 223–227

    Google Scholar 

  • Vazquez E, Bect J (2011) Sequential search based on kriging: convergence analysis of some algorithms. Proceedings of the 58th world statistical congress of the ISI, pp 1241–1250

    Google Scholar 

  • Welch WJ (1985) ACED: algorithms for the construction of experimental designs. Am Stat 39:146

    Article  Google Scholar 

  • Welch WJ, Buck RJ, Sacks J, Wynn HP, Mitchell TJ, Morris MD (1992) Screening, predicting, and computer experiments. Technometrics 34:15–25

    Article  Google Scholar 

  • Wiens DP (1991) Designs for approximately linear regression: Two optimality properties of uniform designs. Stat Probab Lett 12:217–221

    Article  MathSciNet  Google Scholar 

  • Williams BJ, Loeppky JL, Moore LM, Macklem MS (2011) Batch sequential design to achieve predictive maturity with calibrated computer models. Reliab Eng Syst Saf 96(9):1208–1219

    Article  Google Scholar 

  • Wu CFJ, Hamada M (2009) Experiments: planning, analysis, and parameter design optimization, 2nd edn. Wiley, New York, NY

    MATH  Google Scholar 

  • Ye KQ (1998) Orthogonal column Latin hypercubes and their application in computer experiments. J Am Stat Assoc 93:1430–1439

    Article  MathSciNet  Google Scholar 

  • Ye KQ, Li W, Sudjianto A (2000) Algorithmic construction of optimal symmetric Latin hypercube designs. J Stat Plann Inf 90(1):145–159

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media, LLC, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Santner, T.J., Williams, B.J., Notz, W.I. (2018). Space-Filling Designs for Computer Experiments. In: The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8847-1_5

Download citation

Publish with us

Policies and ethics