Statistical Modelling 5 (2005), 53–74
Efficient models for correlated data via convolutions of
intrinsic processes
Herbert K.H. Lee
School of Engineering,
University of California, Santa Cruz,
1156 High Street,
Santa Cruz, CA 95064
USA
eMail:
herbie@ams.ucsc.edu
Dave M. Higdon
Los Alamos National Laboratory,
Los Alamos, New Mexico
USA
Catherine A. Calder
The Ohio State University,
Columbus, Ohio
USA
Christopher H. Holloman
J.P. Morgan Chase,
Columbus, Ohio
USA
Abstract:
Gaussian processes (GP) have proven to be useful and versatile
stochastic models in a wide variety of applications including
computer experiments, environmental monitoring, hydrology and
climate modeling. A GP model is determined by its mean and covariance
functions. In most cases, the mean is specified to be a constant,
or some other simple linear function, whereas the covariance
function is governed by a few parameters. A Bayesian formulation
is attractive as it allows for formal incorporation of uncertainty
regarding the parameters governing the GP. However, estimation of
these parameters can be problematic. Large datasets, posterior
correlation and inverse problems can all lead to difficulties in
exploring the posterior distribution. Here, we propose an alternative
model which is quite tractable computationally – even with large
datasets or indirectly observed data – while still maintaining
the flexibility and adaptiveness of traditional GP models. This model
is based on convolving simple Markov random fields with a smoothing
kernel. We consider applications in hydrology and aircraft prototype
testing.
Keywords:
CONDITIONAL AUTOREGRESSION; INVERSE PROBLEM; MOVING AVERAGE;
NONSTATIONARITY; SPATIAL CORRELATION
Downloads:
R code
including example data
See http://www.r-project.org
for information on the R Project for Statistical Computing.
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