HR: 16:30h
AN: GC52B-03 INVITED     [PDF]
TI: A Hierarchical Bayesian Model for Reconstructing Multiple Streamflows and Climate Indices from Tree-ring or other paleo data
AU: * Lall, U
EM: ula2@columbia.edu
AF: Columbia University, Dept of Earth & Env Eng, 918 Mudd, 500 W 120th St, New York, NY 10027 United States
AU: Zamora, M R
EM: m100874@hotmail.com
AF: Columbia University, LDEO, 64 Rte 9W, Palisades, NY 10964 United States
AU: Cook, E
EM: drdendro@ldeo.columbia.edu
AF: Columbia University, LDEO, 64 Rte 9W, Palisades, NY 10964 United States
AU: Gelman, A
EM: gelman@neyman.stat.columbia.edu
AF: Columbia University, Deprtment of Statistics,, New York, NY 10027
AU: Sperry, E
EM: eesrps@yahoo.com
AF: Columbia University, Dept of Earth & Env Eng, 918 Mudd, 500 W 120th St, New York, NY 10027 United States
AB: Reconstruction of annual or seasonal streamflow at multiple locations or of multiple climatic indices (e.g., PDSI at many locations, or ENSO, PDO, NAO) is sometimes of interest using an array of common paleo predictors. The predictands may be correlated with each other, and the form of each regression between predictand and predictors may also be very similar. Principal or Canonical Component Methods have been used to address this regression problem, after transformation of the data sets to be approximately Normally distributed. An alternative to such methods is presented here. A hierarchical model considers that the regression coefficients are random variables, and seeks to make inferences about the parameters (e.g., they may be Normally distributed, with a certain vector of means and a covariance matrix) of a model that describes the distribution of these variables. Further, the parameters of such a model may in turn be considered to be random variables and one can seek a model that describes them, leading to a multilevel modeling approach. Generally, a diffuse prior distribution is assumed for the parameters at the end of the hierarchy, and a Markov Chain Monte Carlo approach is used to learn or estimate the parameters of the distribution at each level of the hierarchy. Here, we use such an approach in a Generalized Linear Modeling framework - the distribution of the predictand is directly considered to correspond to a parametric family, instead of using transformations to Normality, and a set of basis functions (not necessarily linear) is used to relate the predictors to the predictands. An uncertainty distribution of parameters and hence of estimates is derived automatically as part of the model learning process. We present examples of the applications of these methods and contrast the results with those obtained using PCA/CCA.
DE: 1620 Climate dynamics (3309)
DE: 1655 Water cycles (1836)
DE: 1812 Drought
DE: 1860 Runoff and streamflow
SC: Global Climate Change [GC]
MN: 2003 Fall Meeting