1,754
Views
2
CrossRef citations to date
0
Altmetric
Review Article

Hierarchical modeling of space-time dendroclimatic fields: Comparing a frequentist and a Bayesian approach

ORCID Icon & ORCID Icon
Pages 115-127 | Received 14 Aug 2018, Accepted 14 Feb 2019, Published online: 29 Apr 2019

References

  • Auffhammer, M., B. Li, B. Wright, and S.-J. Yoo. 2015. Specification and estimation of the transfer function in dendroclimatological reconstructions. Environmental and Ecological Statistics 22 (1):105–26. doi:10.1007/s10651-014-0291-6.
  • Banerjee, S., B. P. Carlin, and A. E. Gelfand. 2014. Hierarchical modeling and analysis for spatial data. 2nd ed. New York, New York, USA: Chapman and Hall.
  • Becknell, J. M., A. R. Desai, M. C. Dietze, C. A. Schultz, G. Starr, P. A. Duffy, J. F. Franklin, A. Pourmokhtarian, J. Hall, P. C. Stoy, et al. 2015. Assessing interactions among changing climate, management, and disturbance in forests: A macrosystems approach. Bioscience 65 (3):263–74. doi:10.1093/biosci/biu234.
  • Biondi, F. 2014. Dendroclimatic reconstruction at km-scale grid points: A case study from the Great Basin of North America. Journal of Hydrometeorology 15 (2):891–906. doi:10.1175/JHM-D-13-0151.1.
  • Biondi, F., D. E. Myers, and C. C. Avery. 1994. Geostatistically modeling stem size and increment in an old-growth forest. Canadian Journal of Forest Research 24 (7):1354–68. doi:10.1139/x94-176.
  • Biondi, F., and F. Qeadan. 2008. A theory-driven approach to tree-ring standardization: Definining the biological trend from expected basal area increment. Tree-Ring Research 64 (2):81–96. doi:10.3959/2008-6.1.
  • Biondi, F., and T. W. Swetnam. 1987. Box-Jenkins models of forest interior tree-ring chronologies. Tree-Ring Bulletin 47:71–95.
  • Blangiardo, M., and M. Cameletti. 2015. Spatial and Spatio-temporal Bayesian Models with R - INLA, 308. Chichester, West Sussex, UK: John Wiley & Sons.
  • Blangiardo, M., M. Cameletti, G. Baio, and H. Rue. 2013. Spatial and spatio-temporal models with R-INLA. Spatial and Spatio-Temporal Epidemiology 4:33–49.
  • Bradley, R. S. 2014. Paleoclimatology, 696. 3rd ed. San Diego, California, USA: Academic Press.
  • Brooks, S., A. Gelman, G. L. Jones, and X.-L. Meng. 2011. Handbook of Markov Chain Monte Carlo, 619. Boca Raton, FL: CRC Press, Taylor & Francis Group.
  • Cameletti, M. 2013. Package ‘Stem’: Spatio-temporal models in R, 17. R Foundation for Statistical Computing. https://cran.r-project.org/web/packages/Stem/Stem.pdf.
  • Cameletti, M., F. Lindgren, D. Simpson, and H. Rue. 2013. Spatio-temporal modeling of particulate matter concentration through the SPDE approach. AStA Advances in Statistical Analysis 97 (2):109–31. doi:10.1007/s10182-012-0196-3.
  • Cameletti, M., R. Ignaccolo, and S. Bande. 2011. Comparing spatio-temporal models for particulate matter in Piemonte. Environmetrics 22 (8):985–96. doi:10.1002/env.v22.8.
  • Casella, G., and E. George. 1992. Explaining the Gibbs sampler. The American Statistician 46:167–74.
  • Chib, S., and E. Greenberg. 1995. Understanding the Metropolis-Hastings algorithm. The American Statistician 49:327–35.
  • Clark, J. S., and A. E. Gelfand. 2006. Hierarchical modeling for the environmental sciences: Statistical methods and applications, 216. New York, USA: Oxford University Press.
  • Cook, E. R., K. R. Briffa, D. M. Meko, D. A. Graybill, and G. S. Funkhouser. 1995. The ‘segment length curse’ in long tree-ring chronology development for palaeoclimatic studies. The Holocene 5 (2):229–37. doi:10.1177/095968369500500211.
  • Cressie, N. A. C. 1993. Statistics for spatial data, 900. Rev ed. New York: Wiley-Interscience.
  • Cressie, N. A. C., C. A. Calder, J. S. Clark, J. M. V. Hoef, and C. K. Wikle. 2009. Accounting for uncertainty in ecological analysis: The strengths and limitations of hierarchical statistical modeling. Ecological Applications 19 (3):553–70.
  • Cressie, N. A. C., and C. K. Wikle. 2011. Statistics for spatio-temporal data, 624. Hoboken, NJ: Wiley.
  • Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39 (1):1–38. doi:10.1111/j.2517-6161.1977.tb01600.x.
  • Diggle, P. J., and P. J. Ribeiro. 2007. Model based geostatistics. New York, New York, USA: Springer.
  • Durbin, J., and S. Koopman. 2001. Time series analysis by state space methods. New York, New York, USA: Oxford University Press.
  • Efron, B., and R. J. Tibshirani. 1986. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science 1 (1):54–75. doi:10.1214/ss/1177013815.
  • Fassó, A., and F. Finazzi. 2011. Maximum likelihood estimation of the dynamic coregionalization model with heterotopic data. Environmetrics 22 (6):735–48. doi:10.1002/env.1123.
  • Fassó, A., and M. Cameletti. 2009. The EM algorithm in a distributed computing environment for modelling environmental space-time data. Environmental Modelling & Software 24:1027–35.
  • Fassó, A., and M. Cameletti. 2010. A unified statistical approach for simulation, modeling, analysis and mapping of environmental data. Simulation 86 (3):139–54. doi:10.1177/0037549709102150.
  • Fritts, H. C. 1976. Tree rings and climate, 567. London, UK: Academic Press.
  • Gelfand, A. E. 2012. Hierarchical modeling for spatial data problems. Spatial Statistics 1:30–39.
  • Gelfand, A. E., and A. F. M. Smith. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85 (410):398–409. doi:10.1080/01621459.1990.10476213.
  • Gelfand, A. E., P. J. Diggle, M. Fuentes, and P. Guttorp. 2010. Handbook of spatial statistics.
  • Gelman, A. 2006. Multilevel (hierarchical) modeling: What it can and cannot do. Technometrics 48 (3):432–35. doi:10.1198/004017005000000661.
  • Gelman, A., J. Carlin, H. Stern, D. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis, 675. Boca Raton, FL: CRC Press, Taylor & Francis Group.
  • Gelman, A., and J. Hill. 2006. Data analysis using regression and multilevel/hierarchical models. Cambridge: Cambridge University Press.
  • Gentle, J. E. 2009. Computational statistics, 728. New York, NY: Springer.
  • Girolami, M., and B. Calderhead. 2011. Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (2):123–214. doi:10.1111/rssb.2011.73.issue-2.
  • Gneiting, T. 2002. Nonseparable, stationary covariance functions for space-time data. Journal of the American Statistical Association 97 (458):590–600. doi:10.1198/016214502760047113.
  • Guillot, D., B. Rajaratnam, and J. Emile-Geay. 2015. Statistical paleoclimate reconstructions via Markov random fields. The Annals of Applied Statistics 9 (1):324–52. doi:10.1214/14-AOAS794.
  • Harley, G., C. Baisan, P. Brown, D. Falk, W. Flatley, H. Grissino-Mayer, A. Hessl, E. Heyerdahl, M. Kaye, C. Lafon, et al. 2018. Advancing dendrochronological studies of fire in the United States. Fire 1 (1):art.11 (16 pp.). doi:10.3390/fire1010011.
  • Harvill, J. L. 2010. Spatio-temporal processes. Wiley Interdisciplinary Reviews: Computational Statistics 2 (3):375–82. doi:10.1002/wics.88.
  • Heffernan, J. B., P. A. Soranno, M. J. Angilletta, L. B. Buckley, D. S. Gruner, T. H. Keitt, J. R. Kellner, J. S. Kominoski, A. V. Rocha, J. Xiao, et al. 2014. Macrosystems ecology: Understanding ecological patterns and processes at continental scales. Frontiers in Ecology and the Environment 12 (1):5–14. doi:10.1890/130017.
  • Hoff, P. 2009. A first course in Bayesian statistical methods, 271. New York, NY: Springer.
  • Hughes, M. K., T. W. Swetnam, and H. F. Diaz. 2011. Dendroclimatology: Progress and prospects, 365. Dordrecht: Springer Science+Business Media B.V.
  • Illian, J., A. Penttinen, H. Stoyan, and D. Stoyan. 2008. Statistical analysis and modelling of spatial point patterns, 536. Chichester: Wiley.
  • Isaaks, E. H., and R. M. Srivastava. 1989. An introduction to applied geostatistics. New York: Oxford University Press.
  • Jin, X., B. W. Wah, X. Cheng, and Y. Wang. 2015. Significance and challenges of big data research. Big Data Research 2 (2):59–64. doi:10.1016/j.bdr.2015.01.006.
  • Katz, R. W. 2002. Techniques for estimating uncertainty in climate change scenarios and impact studies. Climate Research 20 (2):167–85. doi:10.3354/cr020167.
  • Katz, R. W., P. F. Craigmile, P. Guttorp, M. Haran, B. Sanso, and M. L. Stein. 2013. Uncertainty analysis in climate change assessments. Nature Climate Change 3 (9):769–71. doi:10.1038/nclimate1980.
  • Körner, C., and E. Hiltbrunner. 2018. The 90 ways to describe plant temperature. Perspectives in Plant Ecology, Evolution and Systematics 30:16–21.
  • Körner, C., and J. Paulsen. 2004. A world-wide study of high altitude treeline temperatures. Journal of Biogeography 31:713–32.
  • Lawson, A. B. 2009. Bayesian disease mapping: Hierarchical modeling in spatial epidemiology, 464. Boca Raton, FL: CRC Press, Taylor & Francis Group.
  • Little, R. J. A., and D. B. Rubin. 2002. Statistical analysis with missing data, 392. 2nd ed. Hoboken, New Jersey, USA: John Wiley & Sons.
  • Mannshardt, E., P. F. Craigmile, and M. P. Tingley. 2013. Statistical modeling of extreme value behavior in North American tree-ring density series. Climatic Change 117 (4):843–58. doi:10.1007/s10584-012-0575-5.
  • McLachlan, G. J., and T. Krishnan. 1997. The EM algorithm and extensions. New York, New York, USA: Wiley.
  • McShane, B. B., and A. J. Wyner. 2011. A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? The Annals of Applied Statistics 5 (1):5–44. doi:10.1214/10-AOAS398.
  • Melvin, T. M., and K. R. Briffa. 2008. A “signal-free” approach to dendroclimatic standardisation. Dendrochronologia 26:71–86. doi:10.1016/j.dendro.2007.12.001.
  • Militino, A. F., M. D. Ugarte, T. Goicoa, and M. Genton. 2015. Interpolation of daily rainfall using spatiotemporal models and clustering. International Journal of Climatology 35 (7):1453–1464.
  • National Research Council. 2006. Surface temperature reconstructions for the last 2,000 years. Washington, DC: The National Academies Press.
  • Neal, R. 2011. MCMC using Hamiltonian dynamics. In Handbook of Markov Chain Monte Carlo, ed. S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng, 113–62. Boca Raton, FL: CRC Press, Taylor & Francis Group.
  • Nilsen, T., J. P. Werner, D. V. Divine, and M. Rypdal. 2018. Assessing the performance of the BARCAST climate field reconstruction technique for a climate with long-range memory. Climate of the Past 14 (6):947–67. doi:10.5194/cp-14-947-2018.
  • Paulsen, J., and C. Körner. 2014. A climate-based model to predict potential treeline position around the globe. Alpine Botany 124 (1):1–12. doi:10.1007/s00035-014-0124-0.
  • R Core Team. 2015. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
  • Rue, H., S. Martino, and N. Chopin. 2009. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society, Series B 2 (71):1–35.
  • Schneider, T. 2001. Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. Journal of Climate 14 (5):853–71. doi:10.1175/1520-0442(2001)014<0853:AOICDE>2.0.CO;2.
  • Schofield, M. R., and R. J. Barker. 2017. Model fitting and evaluation in climate reconstruction of tree-ring data: A comment on Steinschneider et al. (2017): Hierarchical regression models for dendroclimatic standardization and climate reconstruction. Dendrochronologia 46:77–84.
  • Schofield, M. R., R. J. Barker, A. Gelman, E. R. Cook, and K. R. Briffa. 2016. A model-based approach to climate reconstruction using tree-ring data. Journal of the American Statistical Association 111 (513):93–106. doi:10.1080/01621459.2015.1110524.
  • Shaddick, G., and J. V. Zidek. 2014. A case study in preferential sampling: Long term monitoring of air pollution in the UK. Spatial Statistics 9:51–65.
  • Shumway, R. H., and D. S. Stoffer. 2011. Time series analysis and its applications. 3rd ed. New York, New York, USA: Springer Science+Business Media.
  • Steinschneider, S., E. R. Cook, K. R. Briffa, and U. Lall. 2017. Hierarchical regression models for dendroclimatic standardization and climate reconstruction. Dendrochronologia 44:174–86.
  • Tingley, M. P. 2011. A Bayesian ANOVA scheme for calculating climate anomalies, with applications to the instrumental temperature record. Journal of Climate 25 (2):777–91. doi:10.1175/JCLI-D-11-00008.1.
  • Tingley, M. P., and P. Huybers. 2010a. A Bayesian algorithm for reconstructing climate anomalies in space and time. Part II: Comparison with the regularized expectation–Maximization algorithm. Journal of Climate 23:2782–800.
  • Tingley, M. P., and P. Huybers. 2010b. A Bayesian algorithm for reconstructing climate anomalies in space and time. Part I: Development and applications to paleoclimate reconstruction problems. Journal of Climate 23:2759–81.
  • Tingley, M. P., and P. Huybers. 2013. Recent temperature extremes at high northern latitudes unprecedented in the past 600 years. Nature 496 (7444):201–05. doi:10.1038/nature11969.
  • Tingley, M. P., P. F. Craigmile, M. Haran, B. Li, E. Mannshardt, and B. Rajaratnam. 2012. Piecing together the past: Statistical insights into paleoclimatic reconstructions. Quaternary Science Reviews 35:1–22.
  • Tipton, J., M. Hooten, N. Pederson, M. Tingley, and D. Bishop. 2016. Reconstruction of late Holocene climate based on tree growth and mechanistic hierarchical models. Environmetrics 27 (1):42–54. doi:10.1002/env.v27.1.
  • Touchan, R., V. V. Shishov, I. I. Tychkov, F. Sivrikaya, J. Attieh, M. Ketmen, J. Stephan, I. Mitsopoulos, A. Christou, and D. M. Meko. 2016. Elevation-layered dendroclimatic signal in eastern Mediterranean tree rings. Environmental Research Letters 11 (4):044020. doi:10.1088/1748-9326/11/4/044020.
  • Werner, J. P., J. Luterbacher, and J. E. Smerdon. 2012. A pseudoproxy evaluation of Bayesian hierarchical modeling and canonical correlation analysis for climate field reconstructions over Europe. Journal of Climate 26 (3):851–67. doi:10.1175/JCLI-D-12-00016.1.
  • Wikle, C. K. 2003. Hierarchical models in environmental science. International Statistical Review 71:181–99.
  • Wikle, C. K. 2015. Modern perspectives on statistics for spatio-temporal data. Wiley Interdisciplinary Reviews: Computational Statistics 7:86–98.
  • Wikle, C. K., and L. M. Berliner. 2007. A Bayesian tutorial for data assimilation. Physica D: Nonlinear Phenomena 230 (1–2):1–16. doi:10.1016/j.physd.2006.09.017.
  • Wikle, C. K., and N. A. C. Cressie. 1999. A dimension-reduced approach to space-time Kalman filtering. Biometrika 86 (4):812–29. doi:10.1093/biomet/86.4.815.