Fast Nonseparable Gaussian Stochastic Process With Application to Methylation Level Interpolation

References

• Banerjee, S., Gelfand, A. E., Finley, A. O., and Sang, H. (2008), “Gaussian Predictive Process Models for Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 70, 825–848. DOI: 10.1111/j.1467-9868.2008.00663.x.
   Google Scholar
• Bayarri, M. J., Berger, J. O., Calder, E. S., Dalbey, K., Lunagomez, S., Patra, A. K., Pitman, E. B., Spillerh, E. T., and Wolperti, R. L. (2009), “Using Statistical and Computer Models to Quantify Volcanic Hazards,” Technometrics, 51, 402–413. DOI: 10.1198/TECH.2009.08018.
   Web of Science ®Google Scholar
• Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32. DOI: 10.1023/A:1010933404324.
   Web of Science ®Google Scholar
• Chang, W., Haran, M., Olson, R., and Keller, K. (2014), “Fast Dimension-Reduced Climate Model Calibration and the Effect of Data Aggregation,” The Annals of Applied Statistics, 8, 649–673. DOI: 10.1214/14-AOAS733.
   Web of Science ®Google Scholar
• Chu, T., Wang, H., and Zhu, J. (2014), “On Semiparametric Inference of Geostatistical Models via Local Karhunen–Loève Expansion,” Journal of the Royal Statistical Society, Series B, 76, 817–832. DOI: 10.1111/rssb.12053.
   Google Scholar
• Conti, S., and O’Hagan, A. (2010), “Bayesian Emulation of Complex Multi-Output and Dynamic Computer Models,” Journal of Statistical Planning and Inference, 140, 640–651. DOI: 10.1016/j.jspi.2009.08.006.
   Web of Science ®Google Scholar
• Cressie, N., and Johannesson, G. (2008), “Fixed Rank Kriging for Very Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 70, 209–226. DOI: 10.1111/j.1467-9868.2007.00633.x.
   Google Scholar
• Das, P. M., and Singal, R. (2004), “DNA Methylation and Cancer,” Journal of Clinical Oncology, 22, 4632–4642. DOI: 10.1200/JCO.2004.07.151.
   PubMed Web of Science ®Google Scholar
• Eidsvik, J., Shaby, B. A., Reich, B. J., Wheeler, M., and Niemi, J. (2014), “Estimation and Prediction in Spatial Models With Block Composite Likelihoods,” Journal of Computational and Graphical Statistics, 23, 295–315. DOI: 10.1080/10618600.2012.760460.
   Web of Science ®Google Scholar
• Gelfand, A. E., Diggle, P., Guttorp, P., and Fuentes, M. (2010), Handbook of Spatial Statistics, Boca Raton, FL: CRC Press.
   Google Scholar
• Gelfand, A. E., Schmidt, A. M., Banerjee, S., and Sirmans, C. (2004), “Nonstationary Multivariate Process Modeling Through Spatially Varying Coregionalization,” Test, 13, 263–312. DOI: 10.1007/BF02595775.
   Web of Science ®Google Scholar
• Goulard, M., and Voltz, M. (1992), “Linear Coregionalization Model: Tools for Estimation and Choice of Cross-Variogram Matrix,” Mathematical Geology, 24, 269–286. DOI: 10.1007/BF00893750.
   Google Scholar
• Gu, M. (2019a), “FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process,” R Package Version 0.5.1.
   Google Scholar
• Gu, M. (2019b), “Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection,” Bayesian Analysis, 14, 857–885. DOI: 10.1214/18-BA1133.
   Web of Science ®Google Scholar
• Gu, M., and Berger, J. O. (2016), “Parallel Partial Gaussian Process Emulation for Computer Models With Massive Output,” The Annals of Applied Statistics, 10, 1317–1347. DOI: 10.1214/16-AOAS934.
   Web of Science ®Google Scholar
• Gu, M., and Shen, W. (2018), “Generalized Probabilistic Principal Component Analysis of Correlated Data,” arXiv no. 1808.10868.
   Google Scholar
• Gu, M., Wang, X., and Berger, J. O. (2018), “Robust Gaussian stochastic process emulation,” The Annals of Statistics, 46, 3038–3066. DOI: 10.1214/17-AOS1648.
   Web of Science ®Google Scholar
• Hartikainen, J., and Sarkka, S. (2010), “Kalman Filtering and Smoothing Solutions to Temporal Gaussian Process Regression Models,” in 2010 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), IEEE, pp. 379–384.
   Google Scholar
• Higdon, D., Gattiker, J., Williams, B., and Rightley, M. (2008), “Computer Model Calibration Using High-Dimensional Output,” Journal of the American Statistical Association, 103, 570–583. DOI: 10.1198/016214507000000888.
   Web of Science ®Google Scholar
• Kaufman, C. G., Schervish, M. J., and Nychka, D. W. (2008), “Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets,” Journal of the American Statistical Association, 103, 1545–1555. DOI: 10.1198/016214508000000959.
   Web of Science ®Google Scholar
• Liaw, A., and Wiener, M. (2002), “Classification and Regression by Randomforest,” R News, 2, 18–22.
   Google Scholar
• Lindgren, F., Rue, H., and Lindström, J. (2011), “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach,” Journal of the Royal Statistical Society, Series B, 73, 423–498. DOI: 10.1111/j.1467-9868.2011.00777.x.
   Google Scholar
• Ma, P., and Kang, E. L. (2017), “Fused Gaussian Process for Very Large Spatial Data,” arXiv no. 1702.08797.
   Google Scholar
• Petris, G., Petrone, S., and Campagnoli, P. (2009), Dynamic Linear Models, New York: Springer.
   Google Scholar
• R Core Team (2019), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423. DOI: 10.1214/ss/1177012413.
   Google Scholar
• Scarano, M. I., Strazzullo, M., Matarazzo, M. R., and D’Esposito, M. (2005), “DNA Methylation 40 Years Later: Its Role in Human Health and Disease,” Journal of Cellular Physiology, 204, 21–35. DOI: 10.1002/jcp.20280.
   PubMed Web of Science ®Google Scholar
• Shi, T., and Cressie, N. (2007), “Global Statistical Analysis of MISR Aerosol Data: A Massive Data Product From NASA’s Terra Satellite,” Environmetrics, 18, 665–680. DOI: 10.1002/env.864.
   Web of Science ®Google Scholar
• West, M., and Harrison, P. J. (1997), Bayesian Forecasting & Dynamic Models (2nd ed.), New York: Springer-Verlag.
   Google Scholar
• Whittle, P. (1954), “On Stationary Processes in the Plane,” Biometrika, 41, 434–449. DOI: 10.1093/biomet/41.3-4.434.
   Web of Science ®Google Scholar
• Whittle, P. (1963), “Stochastic Process in Several Dimensions,” Bulletin of the International Statistical Institute, 40, 974–994.
   Google Scholar
• Wickham, H. (2007), “Reshaping Data With the Reshape Package,” Journal of Statistical Software, 21, 1–20. DOI: 10.18637/jss.v021.i12.
   Web of Science ®Google Scholar
• Wickham, H. (2016), ggplot2: Elegant Graphics for Data Analysis, New York: Springer-Verlag.
   Google Scholar
• Zhang, W., Spector, T. D., Deloukas, P., Bell, J. T., and Engelhardt, B. E. (2015), “Predicting Genome-Wide DNA Methylation Using Methylation Marks, Genomic Position, and DNA Regulatory Elements,” Genome Biology, 16, 1–20. DOI: 10.1186/s13059-015-0581-9.
   PubMed Web of Science ®Google Scholar
• Ziller, M. J., Gu, H., Müller, F., Donaghey, J., Tsai, L. T.-Y., Kohlbacher, O., De Jager, P. L., Rosen, E. D., Bennett, D. A., Bernstein, B. E., and Gnirke, A. (2013), “Charting a Dynamic DNA Methylation Landscape of the Human Genome,” Nature, 500, 477–481. DOI: 10.1038/nature12433.
   PubMed Web of Science ®Google Scholar