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International Journal for Uncertainty Quantification
IF: 4.911 5-Year IF: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019027823
pages 331-349

PIG PROCESS: JOINT MODELING OF POINT AND INTEGRAL RESPONSES IN COMPUTER EXPERIMENTS

Heng Su
Wells Fargo Bank, Charlotte, NC 28202, USA
Rui Tuo
Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843, USA
C. F. Jeff Wu
The H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

ABSTRACT

Motivated by work on building energy simulation, this paper develops a new class of models called point-integral Gaussian (PIG) processes. The covariance structures of these models are obtained and their parameter estimation and prediction are derived. In the case of axis-parallel rectangular regions, closed form expressions for the covariance functions are obtained. Two simulated examples are used to demonstrate the use of the PIG process models and show their superior performance over those without the integral information.

REFERENCES

  1. Santner, T.J., Williams, B.J., andNotz, W.I., The Design and Analysis of Computer Experiments, Berlin: Springer Science & Business Media, 2013.

  2. Sun, Y., Su, H., Wu, C.F. J., and Augenbroe, G., Quantification of Model Form Uncertainty in the Calculation of Solar Diffuse Irradiation on Inclined Surfaces for Building Energy Simulation, J. Build. Perform. Simul., 8(4):253-265, 2015.

  3. Perez, R., Ineichen, P., Seals, R., Michalsky, J., and Stewart, R., Modeling Daylight Availability and Irradiance Components from Direct and Global Irradiance, Sol. Energy, 44(5):271-289, 1990.

  4. Morris, M.D., Mitchell, T. J., and Ylvisaker, D., Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction, Technometrics, 35(3):243-255, 1993.

  5. Resnick, S.I., A Probability Path, Berlin: Springer Science & Business Media, 2013.

  6. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H.P., Design and Analysis of Computer Experiments, Stat. Sci., 4(4):409-423, 1989.

  7. Rasmussen, C.E., Gaussian Processes for Machine Learning, Cambridge, MA: MIT Press, 2006.

  8. Stein, M.L., Interpolation of Spatial Data: Some Theory for Kriging, Berlin: Springer Science & Business Media, 1999.

  9. Cressie,N.A., Change of Support and the Modifiable Areal Unit Problem, Geograph. Syst., 3(2-3):159-180,1996.

  10. Carlin, B.P., Xia, H., Devine, O., Tolbert, P., and Mulholland, J., Spatio-Temporal Hierarchical Models for Analyzing Atlanta Pediatric Asthma ER Visit Rates, in Case Studies in Bayesian Statistics, Berlin: Springer, pp. 303-320, 1999.

  11. Gelfand, A.E., Zhu, L., and Carlin, B.P., On the Change of Support Problem for Spatio-Temporal Data, Biostatistics, 2(1):31-45,2001.

  12. Cressie, N., Statistics for Spatial Data, New York: John Wiley & Sons, 2015.

  13. Box, G.E.P., Hunter, J.S., and Hunter, W.G., Statistics for Experimenters: Design, Innovation, and Discovery, Vol. 2, New York: Wiley-Interscience, 2005.

  14. Wu, C.F.J. and Hamada, M.S., Experiments: Planning, Analysis, and Optimization, Vol. 552, New York: John Wiley & Sons, 2009.

  15. Sung, C.L., Gramacy, R.B., and Haaland, B., Potentially Predictive Variance Reducing Subsample Locations in Local Gaussian Process Regression, Stat. Sin., 28:577-600,2018.

  16. Haaland, B. and Qian, P.Z.G., Accurate Emulators for Large-Scale Computer Experiments, Ann. Stat:., 39(6):2974-3002, 2011.


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