References
- Aigrain, S., Parviainen, H., and Pope, B. (2016), “K2SC: Flexible Systematics Correction and Detrending of K2 Light Curves Using Gaussian Process Regression,” Monthly Notices of the Royal Astronomical Society, 459, 2408–2419.
- Alexeeff, S. E., Carroll, R. J., and Coull, B. (2016), “Spatial Measurement Error and Correction by Spatial SIMEX in Linear Regression Models When Using Predicted Air Pollution Exposures,” Biostatistics, 17, 377–389. DOI: https://doi.org/10.1093/biostatistics/kxv048.
- Cabral, M. C. (2018), “Quantifying Short-Range Chemical and Structural Order in Complex Oxides via Scanning Transmission Electron Microscopy,” Ph.D. thesis, North Carolina State University.
- Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006), Measurement Error in Nonlinear Models: A Modern Perspective, Boca Raton, FL: Chapman and Hall/CRC.
- Carroll, R. J., and Stefanski, L. A. (1990), “Approximate Quasi-likelihood Estimation in Models With Surrogate Predictors,” Journal of the American Statistical Association, 85, 652–663. DOI: https://doi.org/10.1080/01621459.1990.10474925.
- Chen, I. W., Li, P., and Wang, Y. (1996), “Structural Origin of Relaxor Perovskites,” Journal of Physics and Chemistry of Solids, 57, 1525–1536.
- Cook, J. R., and Stefanski, L. A. (1994), “Simulation-extrapolation Estimation in Parametric Measurement Error Models,” Journal of the American Statistical Association, 89, 1314–1328. DOI: https://doi.org/10.1080/01621459.1994.10476871.
- Cressie, N., and Kornak, J. (2003), “Spatial Statistics in the Presence of Location Error With an Application to Remote Sensing of the Environment,” Statistical Science, 436–456. DOI: https://doi.org/10.1214/ss/1081443228.
- Den Dekker, A., Van Aert, S., Van den Bos, A., and Van Dyck, D. (2005), “Maximum Likelihood Estimation of Structure Parameters From High Resolution Electron Microscopy Images. Part I: A Theoretical Framework,” Ultramicroscopy, 104, 83–106. DOI: https://doi.org/10.1016/j.ultramic.2005.03.001.
- Douglas, S., Agüeros, M., Covey, K., Cargile, P., Barclay, T., Cody, A., Howell, S., and Kopytova, T. (2016), “K2 Rotation Periods for Low-mass Hyads and the Implications for Gyrochronology,” The Astrophysical Journal, 822, 47. DOI: https://doi.org/10.3847/0004-637X/822/1/47.
- Fanshawe, T., and Diggle, P. (2011), “Spatial Prediction in the Presence of Positional Error,” Environmetrics, 22, 109–122. DOI: https://doi.org/10.1002/env.1062.
- Fronterrè, C., Giorgi, E., and Diggle, P. (2018), “Geostatistical Inference in the Presence of Geomasking: A Composite-likelihood Approach,” Spatial Statistics, 28, 319–330. DOI: https://doi.org/10.1016/j.spasta.2018.06.004.
- Gabrosek, J., and Cressie, N. (2002), “The Effect on Attribute Prediction of Location Uncertainty in Spatial Data,” Geographical Analysis, 34, 262–285. DOI: https://doi.org/10.1111/j.1538-4632.2002.tb01088.x.
- Gelfand, A. E., Diggle, P., Guttorp, P., and Fuentes, M. (2010), Handbook of Spatial Statistics, Boca Raton, FL: CRC Press, Chap. 2, pp. 24–26.
- Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013), Bayesian Data Analysis, Boca Raton, FL: CRC Press, Chap. 7, p. 182.
- Gleser, L. (1990), “Improvements of the Naive Approach to Estimation in Nonlinear Errors-in-Variables Regression Models,” Contemporary of Mathematics, 112, 99–114.
- Gryparis, A., Paciorek, C. J., Zeka, A., Schwartz, J., and Coull, B. A. (2008), “Measurement Error Caused by Spatial Misalignment in Environmental Epidemiology,” Biostatistics, 10, 258–274. DOI: https://doi.org/10.1093/biostatistics/kxn033.
- Heaton, M. J., Datta, A., Finley, A. O., Furrer, R., Guinness, J., Guhaniyogi, R., Gerber, F., Gramacy, R. B., Hammerling, D., Katzfuss, M., Lindgren, F., Nychka, D. W., Sun, F., and Zammit-Mangion, A. (2019), “A Case Study Competition Among Methods for Analyzing Large Spatial Data,” Journal of Agricultural, Biological and Environmental Statistics, 24, 1–28. DOI: https://doi.org/10.1007/s13253-018-00348-w.
- Hodges, J. S., and Reich, B. J. (2010), “Adding Spatially-correlated Errors Can Mess Up the Fixed Effect You Love,” The American Statistician, 64, 325–334. DOI: https://doi.org/10.1198/tast.2010.10052.
- Huque, M. H., Bondell, H. D., Carroll, R. J., and Ryan, L. M. (2016), “Spatial Regression With Covariate Measurement Error: A Semiparametric Approach,” Biometrics, 72, 678–686. DOI: https://doi.org/10.1111/biom.12474.
- Jeong, I.-K., Darling, T. W., Lee, J. K., Proffen, T., Heffner, R. H., Park, J. S., Hong, K. S., Dmowski, W., and Egami, T. (2005), “Direct observation of the Formation of Polar Nanoregions in Pb(Mg1/3 Nb2/3 )O3 Using Neutron Pair Distribution Function Analysis,” Physical Review Letters, 94, 147602.
- Katzfuss, M., and Guinness, J. (2017), “A General Framework for Vecchia Approximations of Gaussian Processes,” arXiv preprint arXiv:1708.06302.
- Keen, D. A., and Goodwin, A. L. (2015), “The Crystallography of Correlated Disorder,” Nature, 521, 303–309. DOI: https://doi.org/10.1038/nature14453.
- Kumar, A., Baker, J. N., Bowes, P. C., Cabral, M. J., Zhang, S., Dickey, E. C., Irving, D. L., and LeBeau, J. M. (2020), “Atomic-resolution Electron Microscopy of Nanoscale Local Structure in Lead-based Relax or Ferroelectrics,” Nature Materials, 20, 1–6.
- Larsen, A. E., Reich, B. J., Ruminski, M., and Rappold, A. G. (2018), “Impacts of Fire Smoke Plumes on Regional Air Quality, 2006–2013,” Journal of Exposure Science & Environmental Epidemiology, 28, 319. DOI: https://doi.org/10.1038/s41370-017-0013-x.
- LeBeau, J. M., and Stemmer, S. (2008), “Experimental Quantification of Annular Dark-field Images in Scanning Transmission Electron Microscopy,” Ultramicroscopy, 108, 1653–1658. DOI: https://doi.org/10.1016/j.ultramic.2008.07.001.
- Li, F., Cabral, M. J., Xu, B., Cheng, Z., Dickey, E. C., Lebeau, J. M., Wang, J., Luo, J., Taylor, S., Hackenberger, W., Bellaiche, L., Xu, Z., Chen, L.-q., Shrout, T. R., and Zhang, S. (2019), “Giant Piezoelectricity of Sm-doped Pb(Mg1/3 Nb2/3 )O3-PbTiO3 Single Crystals,” Science, 364, 264– 268.
- Li, Y., Tang, H., and Lin, X. (2009), “Spatial Linear Mixed Models With Covariate Measurement Errors,” Statistica Sinica, 19, 1077–1093.
- Muff, S., Riebler, A., Held, L., Rue, H., and Saner, P. (2015), “Bayesian Analysis of Measurement Error Models Using Integrated Nested Laplace Approximations,” Journal of the Royal Statistical Society, Series C, 64, 231–252. DOI: https://doi.org/10.1111/rssc.12069.
- Paciorek, C. J. (2010), “The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators,” Statistical Science: A Review Journal of the Institute of Mathematical Statistics, 25, 107–125. DOI: https://doi.org/10.1214/10-STS326.
- Schödel, R., Ott, T., Genzel, R., Hofmann, R., Lehnert, M., Eckart, A., Mouawad, N., Alexander, T., Reid, M., Lenzen, R., et al. (2002), “A star in a 15.2-year Orbit Around the Supermassive Black Hole at the Centre of the Milky Way,” Nature, 419, 694–696. DOI: https://doi.org/10.1038/nature01121.
- Stein, M. L. (2014), “Limitations on Low rank Approximations for Covariance Matrices of Spatial Data,” Spatial Statistics, 8, 1–19. DOI: https://doi.org/10.1016/j.spasta.2013.06.003.
- Szpiro, A. A., Sheppard, L., and Lumley, T. (2011), “Efficient Measurement Error Correction With Spatially Misaligned Data,” Biostatistics, 12, 610–623. DOI: https://doi.org/10.1093/biostatistics/kxq083.
- Tadayon, V., and Rasekh, A. (2019), “Non-Gaussian Covariate-Dependent Spatial Measurement Error Model for Analyzing Big Spatial Data,” Journal of Agricultural, Biological and Environmental Statistics, 24, 49–72. DOI: https://doi.org/10.1007/s13253-018-00341-3.
- Tadayon, V., and Torabi, M. (2018), “Spatial Models for Non-Gaussian Data With Covariate Measurement Error,” Environmetrics, e2545. DOI: https://doi.org/10.1002/env.2545.
- Van Aert, S., Den Dekker, A., Van Den Bos, A., Van Dyck, D., and Chen, J. (2005), “Maximum Likelihood Estimation of Structure Parameters From High Resolution Electron Microscopy Images. Part II: A Practical Example,” Ultramicroscopy, 104, 107–125. DOI: https://doi.org/10.1016/j.ultramic.2005.03.002.
- Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
- Vecchia, A. V. (1988), “Estimation and Model Identification for Continuous Spatial Processes,” Journal of the Royal Statistical Society, Series B, 50, 297–312. DOI: https://doi.org/10.1111/j.2517-6161.1988.tb01729.x.