A bayesian algorithm for reconstructing climate anomalies in space and time. Part II: Comparison with the regularized expectation-maximization algorithm

Journal of Climate

Volumn 23, Issue 10, 2010, Pages 2782-2800

  Tingley, Martin P ^a,b   Huybers, Peter ^b  

^a Statistical and Applied Mathematical Sciences Institute USA   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN ALGORITHMS; BAYESIAN APPROACHES; CLIMATE ANOMALIES; DATA COVARIANCE MATRIX; DATA SETS; DATA TYPE; EMPIRICAL ESTIMATE; END-PRODUCTS; EXPECTATION-MAXIMIZATION ALGORITHMS; MULTIVARIATE REGRESSION; OBSERVATION EQUATION; PARAMETRIC FORMS; PRIOR INFORMATION; REGULARIZED EXPECTATION MAXIMIZATIONS; SPACE AND TIME; SPATIAL COVARIANCE; TEMPORAL EVOLUTION; TEMPORAL VARIANCE; UNCERTAINTY INTERVALS;

BAYESIAN NETWORKS; COVARIANCE MATRIX; IMAGE SEGMENTATION; MAXIMUM PRINCIPLE; OPTIMIZATION; REGRESSION ANALYSIS; TIME SERIES; UNCERTAINTY ANALYSIS;

ALGORITHMS;

ALGORITHM; BAYESIAN ANALYSIS; DATA SET; EMPIRICAL ANALYSIS; ESTIMATION METHOD; OBSERVATIONAL METHOD; PROBABILITY; WEATHER FORECASTING;

EID: 77954365677     PISSN: 08948755     EISSN: None     Source Type: Journal    
DOI: 10.1175/2009JCLI3016.1     Document Type: Article

References (40)

1. Anderson, T.,. 2003. An Introduction to Multivariate Statistical Analysis. 3rd ed. Wiley, 752 pp.
2. Banerjee, S., B. P. Carlin, and A. E. Gelfand,. 2004. Hierarchical Modeling and Analysis for SpatialData.Chapman&Hall, 472 pp.
3. Casella, G., and R. Berger,. 2002. Statistical Inference. Thomson Learning Pacific Grove, 700 pp.
4. Cook, E., K. Briffa, and P. Jones,. 1994. Spatial regression methods in dendroclimatology: A review and comparison of two techniques. Int. J. Climatol., 14, 379-402.
5. Cook E. D. Meko, D. Stahle, and M. Cleaveland,. 1999. Drought reconstructions for the continental United States. J. Climate, 12, 1145-1162.
6. Dempster, A. P., N. M. Laird, and D. B. Rubin,. 1977. Maximum likelihood from incomplete data via theEMalgorithm. J. Roy. Stat. Soc., 39, 1-38.
7. Devore, J.,. 1995. Probability and Statistics for Engineering and the Sciences. 4th ed. Brooks/Cole, 750 pp.
8. Fierro, R., G. Golub, P. Hansen, and D. O'Leary,. 1997. Regularization by truncated total least squares. SIAM J. Sci. Comput., 18, 1223-1241.
9. Frost, C., and S. Thompson,. 2000. Correcting for regression dilution bias: Comparison of methods for a single predictor variable. J. Roy. Stat. Soc., 163, 173-189.
10. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin,. 2003. Bayesian Data Analysis. 2nd ed. Chapman & Hall, 696 pp.
11. Golub, G., and C. Van Loan,. 1980. An analysis of the total least squares problem. SIAM J. Numer. Anal., 17, 883-893.
12. Golub, G.,M. Heath, and G. Wahba,. 1979. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21, 215-223.
13. Hegerl, G., and Coauthors,. 2007. Understanding and attributing climate change. Climate Change 2007: The Physical Science Basis. S. Solomon et al., Eds., Cambridge University Press, 663-745.
14. Hoerl, A., and R. Kennard,. 1970. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12, 55-67.
15. Jansen, E., and Coauthors,. 2007. Palaeoclimate. Climate Change 2007: The Physical Science Basis, S. Solomon et al., Eds., Cambridge University Press, 433-498.
16. Jones, P., and Coauthors,. 2009. High-resolution palaeoclimatology of the last millennium: A review of current status and future prospects. Holocene, 19, 3-49, doi:10.1177/0959683608098952.
17. Krakauer, N., T. Schneider, J. Randerson, and S. Olsen,. 2004a. Linear inversion methods and generalized cross-validation. Online supplement to "Using generalized cross-validation to select parameters in inversions for regional carbon fluxes," 7 pp. [Available online at http://ce193.engr.ccny.cuny.edu/papers/GCV_appendix.pdf.]
18. Krakauer, N., T. Schneider, J. Randerson, and S. Olsen,. 2004b. Using generalized cross-validation to select parameters in inversions for regional carbon fluxes. Geophys. Res. Lett., 31, L19108, doi:10.1029/2004GL020323.
19. Lee, T., F. Zwiers, and M. Tsao,. 2008. Evaluation of proxybased millennial reconstruction methods. Climate Dyn., 31, 263-281.
20. Luterbacher, J., D. Dietrich, E. Xoplaki, M. Grosjean, and H. Wanner,. 2004. European seasonal and annual temperature variability, trends, and extremes since 1500. Science, 303, 1499-1503.
21. Mann, M., R. Bradley, and M. Hughes,. 1998. Global-scale temperature patterns and climate forcing over the past six centuries. Nature, 392, 779-787.
22. Mann, M., S. Rutherford, E. Wahl, and C. Ammann,. 2007a. Reply. J. Climate, 20, 5671-5674.
23. Mann, M., S. Rutherford, E. Wahl, and C. Ammann,. 2007b. Robustness of proxy-based climate field reconstruction methods. J. Geophys. Res., 112, D12109, doi:10.1029/2006JD008272.
24. Mann, M., Z. Zhang, M. Hughes, R. Bradley, S. Miller, S. Rutherford, and F. Ni,. 2008. Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. Proc. Natl. Acad. Sci. USA, 105, 13 252-13 257.
25. NRC,. 2006. Surface Temperature Reconstructions for the Last 2000 Years. The National Academies Press, 160 pp.
26. Osborn, T. J., and K. R. Briffa,. 2006. The spatial extent of 20thcentury warmth in the context of the past 1200 years. Science, 311, 841-844.
27. Rubin, D.,. 1976. Inference and missing data. Biometrika, 63, 581-592.
28. Rutherford, S., M. Mann, T. Delworth, and R. Stouffer,. 2003. Climate field reconstruction under stationary and nonstationary forcing. J. Climate, 16, 462-479.
29. Rutherford, S., M. Mann, T. Osborn, R. Bradley, K. Briffa, M. Hughes, and P. Jones,. 2005. Proxy-based Northern Hemisphere surface temperature reconstructions: Sensitivity to method, predictor network, target season, and target domain. J. Climate, 18, 2308-2329.
30. Schneider, T.,. 2001. Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. J. Climate, 14, 853-871.
31. Smerdon, J., and A. Kaplan,. 2007. Comments on "Testing the fidelity of methods used in proxy-based reconstructions of past climate: The role of the standardization interval." J. Climate, 20, 5666-5670.
32. Smerdon, J., and A. Kaplan, D. Chang,. 2008. On the origin of the standardization sensitivity in RegEM climate field reconstructions. J. Climate, 21, 6710-6723.
33. Steig, E., D. Schneider, S. Rutherford, M. Mann, J. Comiso, and D. Shindell,. 2009. Warming of the Antarctic ice-sheet surface since the 1957 International Geophysical Year. Nature, 457, 459-462.
34. Tikhonov, A., and V. Arsenin, 1977: Solutions of Ill-Posed Problems. Winston, 258 pp.
35. Tingley, M., 2009: A Bayesian approach to reconstructing space-time climate fields from proxy and instrumental time series, applied to 600 years of Northern Hemisphere surface temperature data. Ph.D. dissertation, Harvard University, 230 pp.
36. Tingley, M., and P. Huybers, 2010: A Bayesian algorithm for reconstructing climate anomalies in space and time. Part I: Development and applications to paleoclimate reconstruction problems. J. Climate, 23, 2759-2781.
37. van Huffel, S., and J. Vandewalle, 1991: The Total Least Squares Problem: Computational Aspects and Analysis. Society for Industrial Mathematics, 314 pp.
38. von Storch, H., E. Zorita, and F. González-Rouco, 2009: Assessment of three temperature reconstruction methods in the virtual reality of a climate simulation. Int. J. Earth Sci., 98, 67-82.
39. Zar, J. H., 1999: Biostatistical Analysis. 4th ed. Pearson Education, 929 pp.
40. Zhang, Z., M. Mann, and E. Cook, 2004: Alternative methods of proxy-based climate field reconstruction: Application to summer drought over the conterminous United States back to AD 1700 from tree-ring data. Holocene, 14, 502-516.