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Efficient models for correlated data via convolutions of intrinsic processes

School of Engineering, University of California, Santa Cruz, California, USA, herbie{at}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

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.

Key Words: conditional autoregression • inverse problem • moving average • nonstationarity • spatial correlation

Statistical Modelling, Vol. 5, No. 1, 53-74 (2005)
DOI: 10.1191/1471082X05st085oa


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