Bayesian Computation Using Design of Experiments-Based Interpolation Technique

References

• Bishop , C. M. 2006 . Pattern Recognition and Machine Learning , New York : Springer .
   Google Scholar
• Bliznyuk , N. , Ruppert , D. , Shoemaker , C. , Regis , R. , Wild , S. and Mugunthan , P. 2008 . “Bayesian Calibration and Uncertainty Analysis for Computationally Expensive Models Using Optimization and Radial Basis Function Approximation,” . Journal of Computational and Graphical Statistics , 17 : 270 – 294 .
   Web of Science ®Google Scholar
• Bornkamp , B. 2011a . “Approximating Probability Densities by Iterated Laplace Approximations,” . Journal of Computational and Graphical Statistics , 20 : 656 – 669 .
   Web of Science ®Google Scholar
• Bornkamp , B. 2011b . “iterLap: Iterated Laplace approximations, (R package version 1.0-2),” . Available at http://cran.r-project.org/src/contrib/Archive/iterLap/
   Google Scholar
• Brooks , S. , Gelman , A. , Jones , G. L. and Meng , X.-L. 2011 . Handbook of Markov Chain Monte Carlo , Boca Raton, FL : CRC Press .
   Google Scholar
• Buhmann , M. D. 2003 . Radial Basis Functions: Theory and Implementations , Cambridge : Cambridge University Press .
   Google Scholar
• Carnell , R. 2009 . “lhs: Latin hypercube samples (R package version 0.5),” . Available at http://cran.r-project.org/src/contrib/Archive/lhs/
   Google Scholar
• Cohn , D. A. 1996 . “Neural Network Exploration Using Optimal Experimental Design,” . Advances in Neural Information Processing Systems , 6 : 679 – 686 .
   Google Scholar
• Dasgupta , T. , Weintraub , B. and Joseph , V. R. 2011 . “A Physical-Statistical Model for Density Control of Zinc Oxide Nanowires,” . IIE Transactions on Quality and Reliability Engineering , 43 : 233 – 241 .
   Web of Science ®Google Scholar
• Fedorov , V. V. 1972 . Theory of Optimal Experiments , New York : Academic Press .
   Google Scholar
• Fielding , M. 2010 . “MCMChybridGP: Hybrid Markov chain Monte Carlo using Gaussian processes (R package version 3.1),” . Available at http://cran.r-project.org/
   Google Scholar
• Fielding , M. , Nott , D. J. and Liong , S-Y . 2011 . “Efficient MCMC Schemes for Computationally Expensive Posterior Distributions,” . Technometrics , 53 : 16 – 28 .
   Web of Science ®Google Scholar
• Gelfand , A. E. , Hills , S. E. , Racine-Poon , A. and Smith , A. F. M. 1990 . “Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling,” . Journal of the American Statistical Association , 85 : 972 – 985 .
   Web of Science ®Google Scholar
• Gelfand , A. E. and Smith , A. F. M. 1990 . “Sampling-Based Approaches to Calculating Marginal Densities,” . Journal of the American Statistical Association , 85 : 398 – 409 .
   Web of Science ®Google Scholar
• Geman , S. and Geman , D. 1984 . “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images,” . IEEE Transactions on Pattern Analysis and Machine Intelligence , 6 : 721 – 741 .
   PubMed Web of Science ®Google Scholar
• Gramacy , R. B. and Lee , H. K. H. 2009 . “Adaptive Design and Analysis of Supercomputer Experiments,” . Technometrics , 51 : 130 – 145 .
   Web of Science ®Google Scholar
• Haaland , B. and Qian , P. Z. G. 2011 . “Accurate Emulators for Large-Scale Computer Experiments,” . The Annals of Statistics , 39 : 2974 – 3002 .
   Web of Science ®Google Scholar
• Haario , H. , Saksman , E. and Tamminen , J. 2001 . “An Adaptive Metropolis Algorithm,” . Bernoulli , 7 : 223 – 242 .
   Web of Science ®Google Scholar
• Hastings , W. K. 1970 . “Monte Carlo Sampling Methods Using Markov Chain and Their Applications,” . Biometrika , 87 : 97 – 109 .
   Web of Science ®Google Scholar
• Henderson , D. A. , Boys , R. J. , Krishnan , K. J. , Lawless , C. and Wilkinson , D. J. 2009 . “Bayesian Emulation and Calibration of a Stochastic Computer Model of Mitochondrial DNA Deletions in Substantia Nigra Neurons,” . Journal of the American Statistical Association , 104 : 76 – 87 .
   Web of Science ®Google Scholar
• Jaakkola , T. S. and Jordan , M. I. 2000 . “Bayesian Parameter Estimation via Variational Methods,” . Statistics and Computing , 10 : 25 – 37 .
   Web of Science ®Google Scholar
• Johnson , S. G. and Narasimhan , B. 2009 . “cubature: Adaptive multivariate integration over hypercubes (R package version 1.0),” . Available at http://cran.r-project.org/
   Google Scholar
• Joseph , V. R. 2006 . “Limit Kriging,” . Technometrics , 48 : 458 – 466 .
   Web of Science ®Google Scholar
• Kennedy , M. 1998 . “Bayesian Quadrature With Non-Normal Approximating Functions,” . Statistics and Computing , 8 : 365 – 375 .
   Google Scholar
• Kuss , M. and Rasmussen , C. E. 2005 . “Assessing Approximate Inference for Binary Gaussian Process Classification,” . Journal of Machine Learning Research , 6 : 1679 – 1704 .
   Web of Science ®Google Scholar
• Loeppky , J. L. , Sacks , J. and Welch , W. J. 2009 . “Choosing the Sample Size of a Computer Experiment: A Practical Guide,” . Technometrics , 51 : 366 – 376 .
   Web of Science ®Google Scholar
• MacKay , D. J. C. 1992 . “Information-Based Objective Functions for Active Data Selection,” . Neural Computation , 4 : 590 – 604 .
   Web of Science ®Google Scholar
• Marin , J-M and Robert , C. P. 2007 . Bayesian Core: A Practical Approach to Computational Bayesian Statistics , New York : Springer .
   Google Scholar
• Metropolis , N. , Rosenbluth , A. W. , Rosenbluth , M. N. , Teller , A. H. and Teller , E. 1953 . “Equation of State Calculation by Fast Computing Machines,” . Journal of Chemical Physics , 21 : 1087 – 1092 .
   Google Scholar
• Minka , P. 2001 . “Expectation Propagation for Approximate Bayesian Inference,” . Uncertainty in Artificial Intelligence , 17 : 362 – 369 .
   Google Scholar
• Morris , M. D. and Mitchell , T. J. 1995 . “Exploratory Designs for Computer Experiments,” . Journal of Statistical Planning and Inference , 43 : 381 – 402 .
   Web of Science ®Google Scholar
• Naylor , J. C. and Smith , A. F. M. 1982 . “Applications of a Method for the Efficient Computation of Posterior Distributions,” . Applied Statistics , 31 : 214 – 225 .
   Web of Science ®Google Scholar
• O’Hagan , A. 1991 . “Bayes-Hermite Quadrature,” . Journal of Statistical Planning and Inference , 29 : 245 – 260 .
   Web of Science ®Google Scholar
• Ormerod , J. T. and Wand , M. P. 2010 . “Explaining Variational Approximations,” . The American Statistician , 64 : 140 – 153 .
   Web of Science ®Google Scholar
• Ormerod , J. T. and Wand , M. P. 2012 . “Gaussian Variational Approximate Inference for Generalized Linear Mixed Models,” . Journal of Computational and Graphical Statistics , 21 ( 1 ) : 2 – 17 .
   Web of Science ®Google Scholar
• Pinheiro , J. C. and Bates , D. M. 2000 . Mixed-Effects Models in S and S-PLUS , New York : Springer .
   Google Scholar
• Rasmussen , C. E. 2003 . “Gaussian Processes to Speed Up Hybrid Monte Carlo for Expensive Bayesian Integrals,” . In Bayesian Statistics 7 Edited by: Bernardo , J. M. , Bayarri , M. J. , Berger , J. O. , Dawid , A. P. , Heckerman , D. , Smith , A. F. M. and West , M. 651 – 659 .
   Google Scholar
• Rasmussen , C. E. and Ghahramani , Z. 2003 . “Bayesian Monte Carlo,” . In Advances in Neural Information Processing Systems (Vol. 15) , Edited by: Becker , S. T. S. and Obermayer , K. 489 – 496 . Cambridge , MA : MIT Press .
   Google Scholar
• Rasmussen , C. E. and Williams , C. K. I. 2006 . Gaussian Processes for Machine Learning , Cambridge, , MA : MIT Press .
   Google Scholar
• Rue , H. , Martino , S. and Chopin , N. 2009 . “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations” (with discussion) . Journal of the Royal Statistical Society, Series B , 71 : 319 – 392 .
   Web of Science ®Google Scholar
• Santner , T. J. , Williams , B. J. and Notz , W. I. 2003 . The Design and Analysis of Computer Experiments , New York : Springer .
   Google Scholar
• Singh , R. K. , Joseph , V. R. and Melkote , S. N. 2011 . “A Statistical Approach to the Optimization of a Laser-Assisted Micromachining Process,” . International Journal of Advanced Manufacturing Technology , 53 : 221 – 230 .
   Web of Science ®Google Scholar
• Tanner , M. and Wong , W. 1987 . “The Calculation of Posterior Distributions by Data Augmentation” (with discussion) . Journal of the American Statistical Association , 82 : 528 – 550 .
   Web of Science ®Google Scholar
• Tierney , L. and Kadane , J. B. 1986 . “Accurate Approximations for Posterior Moments and Marginal Densities,” . Journal of the American Statistical Association , 81 : 82 – 86 .
   Web of Science ®Google Scholar