In this paper we discuss how a Gaussian random field with Matérn covariance function can represent our prior uncertainty about the log-spectral density, $g(\omega)$, of a Gaussian, short memory time series. Hyperparameters can be suitably tuned in order to determine the mean square differentiability and the range of autocorrelation of the random field $g(\omega)$. However, Bayesian computations cannot be easily performed under such prior elicitations. We suggest therefore to approximate the Gaussian random field priors with a class of Gaussian Markov random fields which preserve the main features of the genuine prior distributions.
Random field priors for spectral density functions
TONELLATO, Stefano Federico
2007-01-01
Abstract
In this paper we discuss how a Gaussian random field with Matérn covariance function can represent our prior uncertainty about the log-spectral density, $g(\omega)$, of a Gaussian, short memory time series. Hyperparameters can be suitably tuned in order to determine the mean square differentiability and the range of autocorrelation of the random field $g(\omega)$. However, Bayesian computations cannot be easily performed under such prior elicitations. We suggest therefore to approximate the Gaussian random field priors with a class of Gaussian Markov random fields which preserve the main features of the genuine prior distributions.File | Dimensione | Formato | |
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