Generalized Integrated Brownian Fields for Simulation Metamodeling

References

• Ankenman B, Nelson BL, Staum J (2010) Stochastic kriging for simulation metamodeling. Oper. Res. 58(2):371–382.Link, Google Scholar
• Aydin G, Porteus EL (2008) Joint inventory and pricing decisions for an assortment. Oper. Res. 56(5):1247–1255.Link, Google Scholar
• Berlinet A, Thomas-Agnan C (2004) Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic Publishers, New York).Crossref, Google Scholar
• Binois M, Gramacy RB, Ludkovski M (2018) Practical heteroskedastic Gaussian process modeling for large simulation experiments. J. Comput. Graphical Statist. 27(4):808–821.Crossref, Google Scholar
• Chen X, Ankenman B, Nelson BL (2012) The effects of common random numbers of stochastic kriging metamodels. ACM Trans. Modeling Comput. Simulation 22(2):1–20.Crossref, Google Scholar
• Chen X, Ankenman B, Nelson BL (2013) Enhancing stochastic kriging metamodels with gradient estimators. Oper. Res. 61(2):512–528.Link, Google Scholar
• Fill JA, Torcaso F (2004) Asymptotic analysis via Mellin transforms for small deviations in l2-norm of integrated Brownian sheets. Probab. Theory Related Fields 130(2):259–288.Crossref, Google Scholar
• Glasserman P, Kang W, Shahabuddin P (2008) Fast simulation of multifactor portfolio credit risk. Oper. Res. 56(5):1200–1217.Link, Google Scholar
• Holden H, Øksendal B, Ubøe J, Zhang T (2010) Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, 2nd ed., Universitext (Springer Science and Business Media, New York).Crossref, Google Scholar
• Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4):455–492.Crossref, Google Scholar
• Joseph VR (2006) Limit kriging. Technometrics 48(4):458–466.Crossref, Google Scholar
• Joseph VR, Hung Y, Sudjianto A (2008) Blind kriging. J. Mech. Design 130(3):031102-1–031102-8.Crossref, Google Scholar
• Kleijnen J, van Beers W (2005) Robustness of kriging when interpolating in random simulation with heterogeneous variance: Some experiments. Eur. J. Oper. Res. 165(3):826–834.Crossref, Google Scholar
• Krige DG (1951) A statistical approach to some mine valuations and allied problems at the Witwatersrand. Master’s thesis, University of Witwatersrand, Johannesburg, South Africa.Google Scholar
• Li R, Sudjianto A (2005) Analysis of computer experiments using penalized likelihood in Gaussian kriging models. Technometrics 47(2):111–120.Crossref, Google Scholar
• Liu M, Staum J (2010) Stochastic kriging for efficient nested simulation of expected shortfall. J. Risk 12(3):3–27.Crossref, Google Scholar
• Mitchell TJ, Morris MD (1992) The spatial correlation function approach to response surface estimation. Proc. 1992 Winter Simulation Conf. (IEEE, Piscataway, NJ), 565–571.Crossref, Google Scholar
• Paciorek CJ, Schervish MJ (2004) Nonstationary covariance functions for Gaussian process regression. Proc. Conf. Neural Inform. Processing Systems (MIT Press, Cambridge, MA).Google Scholar
• Pitt LD (1971) A Markov property for Gaussian processes with a multidimensional parameter. Archive Ration. Mech. Anal. 43(5):367–391.Crossref, Google Scholar
• Powell WB, Ryzhov IO (2012) Optimal Learning (John Wiley and Sons, Hoboken, NJ).Crossref, Google Scholar
• Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Statist. Sci. 4(4):409–423.Crossref, Google Scholar
• Salemi P, Staum J, Nelson BL (2013) Generalized integrated Brownian fields for simulation metamodeling. Proc. 2013 Winter Simulation Conf. (IEEE, Piscataway, NJ).Crossref, Google Scholar
• Santner TJ, Williams BJ, Notz WI (2010) The Design and Analysis of Computer Experiments (Springer, New York).Google Scholar
• Shao J (2010) Mathematical Statistics (Springer Texts in Statistics, New York).Google Scholar
• Sun L, Hong LJ, Hu Z (2014) Balancing exploitation and exploration in discrete optimization via simulation through a Gaussian process-based search. Oper. Res. 62(6):1416–1438.Link, Google Scholar
• van Beers W, Kleijnen J (2003) Kriging for interpolation in random simulation. J. Oper. Res. Soc. 54(3):255–262.Crossref, Google Scholar
• Xie W, Nelson BL, Staum J (2010) The influence of correlation functions on stochastic kriging metamodels. Proc. 2010 Winter Simulation Conf. (IEEE, Piscataway, NJ).Crossref, Google Scholar
• Yin J, Ng SH, Ng KM (2011) Kriging metamodel with modified nugget-effect: The heteroscedastic variance case. Comput. Indust. Engrg. 61(3):760–777.Crossref, Google Scholar
• Zhang N, Apley DW (2014) Fractional Brownian fields for response surface metamodeling. J. Quality Tech. 46(4):285–301.Crossref, Google Scholar
• Zhang N, Apley DW (2016) Brownian integrated covariance functions for Gaussian process modeling: Sigmoidal versus localized basis functions. J. Amer. Statist. Assoc. 111(515):1182–1195.Crossref, Google Scholar