1. Tony O’Hagan reading list. Suggested by Tony O’Hagan for MUCM.
   

2. A Linear Bayes Methodology reading list, suggested by Michael Goldstein

3. SAVE methodology from NISS project (NISS/SAMSI/Duke group).

   1. A preliminary 2002 Technical Report evolved into two shorter 2005 technical reports:

   2.   A Framework for evaluation of computer models, which specifies the methodology and gives a couple of examples (one of them an easy “pedagogical” or “toy” example, absent in the original report), and

   3.  Bayesian Validation of a Computer Model for Vehicle Crashworthiness, for smooth functional outputs and hierarchical Bayes analysis for outputs from related models or untried situations.

   4. A third Technical Report Computer Model Validation with functional Output deals with ‘rough’ functional outputs, uncertainty in the ‘controlable’ inputs, and with issues of extrapolation.
      

   5. Our analysis of the SANDIA challenge,  in which each field data has different values for the calibration parameter, is available here.

4. Statistical Sciences Group at Los Alamos National Laboratory
   

   1. D. Higdon, J. Gattiker and B. Williams (2005). Computer Model Calibration using High Dimensional Output. Explains a basis approach for dealing with high dimensional output. A slide on this approach is available here.
      

   2. D. Higdon, C. Nakhleh, J. Gattiker and B. Williams (2007). A Bayesian Calibration Approach to the Thermal Problem. LANL's solution to the V and V Challenge problem.

   3. K. Heitmann, D. Higdon, C. Nakhleh and S. Habib (2006). Cosmic Calibration. An application in cosmology.

   4. B. Williams, D. Higdon, J. Gattiker, L. Moore, M. D. McKay and S. Keller-McNulty (2006). Combining Experimental Data and Computer Simulations, with an Application to Flyer Plate Experiments. This uses a kronecker approach to deal with the time series output.

   5. M. A. Christie, J. Glimm, J. W. Grove, D. Higdon, D. H. Sharp, M. M. Wood-Schultz (2005). Error Analysis and Simulation of Complex Phenomena, in Los Alamos Science. From a different contingent at LANL; gives a slightly different perspective.

   6. D. Higdon, M. Kennedy, J. Cavendish, John Cafeo and R. D. Ryne (2003). Combining Field Data and Computer Simulations for Calibration and Prediction. A basic 1-d formulation which is very similar to the first SAMSI papers. Looks at the spotwelding application as well as one in modeling a linear accelerator.

5. Herbie Lee’s Treed Gaussian Processes to deal with non stationary simulators
   

   1. Robert B. Gramacy and Herbert K. H. Lee (2006).  Bayesian treed Gaussian process models ---This is the main reference for treed Gaussian Processes.

   2. Robert B. Gramacy and Herbert K. H. Lee (2006). Adaptive design of supercomputer experiments. --- This is the main reference for adaptive sampling (using the results of a treed GP emulator to help choose new run locations)

Treed GPs and some of the adaptive design computations are in the R package tgp, which can be accessed from within R using install.packages("tgp") or from the CRAN website.

  9. Quantile Regression. A couple summary papers on quantile regreesions are those of Koenker and Hallock (2001) and Cade and Noon (2003); an implementation in R appears in Koenker (2006) .

 10. Non-Gaussian Spatial Processes.  Diggle et al. (1998) dicusses Generalized linear mixed model for Geostatistics.

 11. Tapering. Kaufman (2007) is considering using Covariance Tapering method to build efficient emulators for computer experiments. Two revelant papers are: Wendland (1995) introduces Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Wendland (1998) discusses error estimates for interpolation by compactly supported radial basis functions of minimal degree.

 12. The link to the Gaussian Process website is here.

 13.- Use of derivatives (list provided by Tom Loredo).

        1 -  O'Hagan, A. (1992). Some Bayesian numerical analysis (with discussion). In Bayesian Statistics 4, (J. M. Bernardo et al Eds.), 345--363. Oxford University Press.
        2 - M. D. Morris, T. J. Mitchell, D. Ylvisaker (1993).  Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction. Technometrics 35, 243-255.
        3 - K. V. Mardia, J. T. Kent, C. R. Goodall, and J. A. Little (1996).  Kriging and splines with derivative information. Biometrika, 83, 207-221.
        4 - D. J. Leith, W. E. Leithead, E. Solak, R. Murray-Smith (2002).  Divide and conquer: identification using Gaussian process priors. Proceedings of the 41st IEEE Conference on Decision and Control, 624-629.
       5- R. Murray-Smith and B. A. Pearlmutter (2003).  Transformations of Gaussian Process Priors. Tech report
       6 - E. Solak et al. (2003).  Derivative observations in Gaussian Process Models of Dynamic Systems. NIPS
       7 - J. Kocijan, A. Girard, and D. J. Leith (2003).  Incorporating Linear Local Models in Gaussian Process Model. Tech report.
       8 - K. Azman and J. Kocijan (2005).  Comprising Prior Knowledge in Dynamic Gaussian Process Models. CompSysTech 2005 Proceedings.
       9 - P. Hall and A. Yatchew (2007).  Nonparametric estimation when data on derivatives are available; to appear in Annals of Statistics, volume 35, 1. This paper deals with frequentist nonparametric estimation with derivative data. They show that knowing just first derivatives dramatically improves the convergence rate of nonparametric estimators such as KDEs, local polynomials, and splines (GP are not considered). If you know just some first derivatives, the improvement still holds, though only in the directions for which you have the derivative info.