A General Framework for Vecchia Approximations of Gaussian Processes
Tóm tắt
Từ khóa
Tài liệu tham khảo
Varin, C., Reid, N. and Firth, D. (2011). An overview of composite likelihood methods. <i>Statist. Sinica</i> <b>21</b> 5–42.
Banerjee, S., Carlin, B. P. and Gelfand, A. E. (2015). <i>Hierarchical Modeling and Analysis for Spatial Data</i>, 2nd ed. <i>Monographs on Statistics and Applied Probability</i> <b>135</b>. CRC Press, Boca Raton, FL.
Wikle, C. K. and Cressie, N. (1999). A dimension-reduced approach to space-time Kalman filtering. <i>Biometrika</i> <b>86</b> 815–829.
Datta, A., Banerjee, S., Finley, A. O. and Gelfand, A. E. (2016a). Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets. <i>J. Amer. Statist. Assoc.</i> <b>111</b> 800–812.
Du, J., Zhang, H. and Mandrekar, V. S. (2009). Fixed-domain asymptotic properties of tapered maximum likelihood estimators. <i>Ann. Statist.</i> <b>37</b> 3330–3361.
Eidsvik, J., Shaby, B. A., Reich, B. J., Wheeler, M. and Niemi, J. (2014). Estimation and prediction in spatial models with block composite likelihoods. <i>J. Comput. Graph. Statist.</i> <b>23</b> 295–315.
Furrer, R., Genton, M. G. and Nychka, D. (2006). Covariance tapering for interpolation of large spatial datasets. <i>J. Comput. Graph. Statist.</i> <b>15</b> 502–523.
Gramacy, R. B. and Apley, D. W. (2015). Local Gaussian process approximation for large computer experiments. <i>J. Comput. Graph. Statist.</i> <b>24</b> 561–578.
Kaufman, C. G., Schervish, M. J. and Nychka, D. W. (2008). Covariance tapering for likelihood-based estimation in large spatial data sets. <i>J. Amer. Statist. Assoc.</i> <b>103</b> 1545–1555.
Sang, H. and Huang, J. Z. (2012). A full scale approximation of covariance functions for large spatial data sets. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>74</b> 111–132.
Stein, M. L. (2014). Limitations on low rank approximations for covariance matrices of spatial data. <i>Spat. Stat.</i> <b>8</b> 1–19.
Vecchia, A. V. (1988). Estimation and model identification for continuous spatial processes. <i>J. Roy. Statist. Soc. Ser. B</i> <b>50</b> 297–312.
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. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>73</b> 423–498.
Shaby, B. A. (2014). The open-faced sandwich adjustment for MCMC using estimating functions. <i>J. Comput. Graph. Statist.</i> <b>23</b> 853–876.
Banerjee, S., Gelfand, A. E., Finley, A. O. and Sang, H. (2008). Gaussian predictive process models for large spatial data sets. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>70</b> 825–848.
Cressie, N. and Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>70</b> 209–226.
Finley, A. O., Sang, H., Banerjee, S. and Gelfand, A. E. (2009). Improving the performance of predictive process modeling for large datasets. <i>Comput. Statist. Data Anal.</i> <b>53</b> 2873–2884.
Nychka, D., Bandyopadhyay, S., Hammerling, D., Lindgren, F. and Sain, S. (2015). A multiresolution Gaussian process model for the analysis of large spatial datasets. <i>J. Comput. Graph. Statist.</i> <b>24</b> 579–599.
Sang, H., Jun, M. and Huang, J. Z. (2011). Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors. <i>Ann. Appl. Stat.</i> <b>5</b> 2519–2548.
Higdon, D. (1998). A process-convolution approach to modelling temperatures in the North Atlantic Ocean. <i>Environ. Ecol. Stat.</i> <b>5</b> 173–190.
Heaton, M. J., Datta, A., Finley, A. O., Furrer, R., Guinness, J., Guhaniyogi, R., Gerber, F., Gramacy, R. B., Hammerling, D. et al. (2019). A case study competition among methods for analyzing large spatial data. <i>J. Agric. Biol. Environ. Stat.</i> <b>24</b> 398–425.
Rue, H. and Held, L. (2005). <i>Gaussian Markov Random Fields: Theory and Applications</i>. <i>Monographs on Statistics and Applied Probability</i> <b>104</b>. CRC Press/CRC, Boca Raton, FL.
Stein, M. L., Chi, Z. and Welty, L. J. (2004). Approximating likelihoods for large spatial data sets. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>66</b> 275–296.
Gramacy, R. B. and Lee, H. K. H. (2012). Cases for the nugget in modeling computer experiments. <i>Stat. Comput.</i> <b>22</b> 713–722.
Furrer, R. and Sain, S. R. (2010). spam: A sparse matrix R package with emphasis on MCMC methods for Gaussian Markov random fields. <i>J. Stat. Softw.</i> <b>36</b> 1–25.
Rütimann, P. and Bühlmann, P. (2009). High dimensional sparse covariance estimation via directed acyclic graphs. <i>Electron. J. Stat.</i> <b>3</b> 1133–1160.
Rasmussen, C. E. and Williams, C. K. I. (2006). <i>Gaussian Processes for Machine Learning</i>. <i>Adaptive Computation and Machine Learning</i>. MIT Press, Cambridge, MA.
Cressie, N. and Wikle, C. K. (2011). <i>Statistics for Spatio-Temporal Data</i>. <i>Wiley Series in Probability and Statistics</i>. Wiley, Hoboken, NJ.
Katzfuss, M. and Gong, W. (2020). A class of multi-resolution approximations for large spatial datasets. <i>Statist. Sinica</i>. <b>30</b> 2203–2226.
Katzfuss, M., Guinness, J., Gong, W. and Zilber, D. (2020). Vecchia approximations of Gaussian-process predictions. <i>J. Agric. Biol. Environ. Stat.</i>. <b>25</b> 383–414.
Rue, H. and Held, L. (2010). Discrete spatial variation. In <i>Handbook of Spatial Statistics</i>. <i>Chapman & Hall/CRC Handb. Mod. Stat. Methods</i> 171–200. CRC Press, Boca Raton, FL.
Snelson, E. and Ghahramani, Z. (2007). Local and global sparse Gaussian process approximations. In <i>Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics (AISTATS)</i> 524–531.
Zhang, H. (2012). Asymptotics and computation for spatial statistics. In <i>Advances and Challenges in Space-Time Modelling of Natural Events</i> 239–252. Springer, Berlin.
Lauritzen, S. L. (1996). <i>Graphical Models</i>. <i>Oxford Statistical Science Series</i> <b>17</b>. The Clarendon Press, Oxford University Press, New York.
Cressie, N. and Davidson, J. L. (1998). Image analysis with partially ordered Markov models. <i>Comput. Statist. Data Anal.</i> <b>29</b> 1–26.
Datta, A., Banerjee, S., Finley, A. O. and Gelfand, A. E. (2016b). On nearest-neighbor Gaussian process models for massive spatial data. <i>Wiley Interdiscip. Rev.: Comput. Stat.</i> <b>8</b> 162–171.
Datta, A., Banerjee, S., Finley, A. O., Hamm, N. A. S. and Schaap, M. (2016c). Nonseparable dynamic nearest neighbor Gaussian process models for large spatio-temporal data with an application to particulate matter analysis. <i>Ann. Appl. Stat.</i> <b>10</b> 1286–1316.
Eubank, R. L. and Wang, S. (2002). The equivalence between the Cholesky decomposition and the Kalman filter. <i>Amer. Statist.</i> <b>56</b> 39–43.
Finley, A. O., Datta, A., Cook, B. C., Morton, D. C., Andersen, H. E. and Banerjee, S. (2019). Efficient algorithms for Bayesian nearest neighbor Gaussian processes. <i>J. Comput. Graph. Statist.</i> <b>28</b> 401–414.
Gerber, F., Furrer, R., Schaepman-Strub, G., de Jong, R. and Schaepman, M. E. (2018). Predicting missing values in spatio-temporal satellite data. <i>IEEE Trans. Geosci. Remote Sens.</i> <b>56</b> 2841–2853.
Guhaniyogi, R. and Banerjee, S. (2018). Meta-kriging: Scalable Bayesian modeling and inference for massive spatial datasets. <i>Technometrics</i> <b>60</b> 430–444.
Guinness, J. (2018). Permutation and grouping methods for sharpening Gaussian process approximations. <i>Technometrics</i> <b>60</b> 415–429.
Huang, H. and Sun, Y. (2018). Hierarchical low rank approximation of likelihoods for large spatial datasets. <i>J. Comput. Graph. Statist.</i> <b>27</b> 110–118.
Jurek, M. and Katzfuss, M. (2018). Multi-resolution filters for massive spatio-temporal data. Available at <a href="arXiv:1810.04200">arXiv:1810.04200</a>.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. <i>Trans. ASME Ser. D. J. Basic Eng.</i> <b>82</b> 35–45.
Katzfuss, M. (2017). A multi-resolution approximation for massive spatial datasets. <i>J. Amer. Statist. Assoc.</i> <b>112</b> 201–214.
Katzfuss, M. and Cressie, N. (2011). Spatio-temporal smoothing and EM estimation for massive remote-sensing data sets. <i>J. Time Series Anal.</i> <b>32</b> 430–446.
Minden, V., Damle, A., Ho, K. L. and Ying, L. (2017). Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations. <i>Multiscale Model. Simul.</i> <b>15</b> 1584–1611.
Quiñonero-Candela, J. and Rasmussen, C. E. (2005). A unifying view of sparse approximate Gaussian process regression. <i>J. Mach. Learn. Res.</i> <b>6</b> 1939–1959.
Rauch, H. E., Tung, F. and Striebel, C. T. (1965). Maximum likelihood estimates of linear dynamic systems. <i>AIAA J.</i> <b>3</b> 1445–1450.
Stein, M. L. (2011). 2010 Rietz Lecture: When does the screening effect hold? <i>Ann. Statist.</i> <b>39</b> 2795–2819.
Sun, Y. and Stein, M. L. (2016). Statistically and computationally efficient estimating equations for large spatial datasets. <i>J. Comput. Graph. Statist.</i> <b>25</b> 187–208.
Toledo, S. (2007). Lecture notes on combinatorial preconditioners, Chapter 3. Available at <a href="http://www.tau.ac.il/~stoledo/Support/chapter-direct.pdf">http://www.tau.ac.il/~stoledo/Support/chapter-direct.pdf</a>.