I apologize in advance because my question(s) are not specific to
Splus.
A colleague of mine and I have implemented a Metropolis-Hastings
algorithm to estimate a spatial autoregressive (SAR) lattice model. Two
books, one by Dani Gamerman and the other by Casella & Robert,
formed the basis of our implementation. We are convinced that
this algorithm is working well on the basis of some validations using
simple models with known results.
The difficultly is that our spatial model exists on a 2184 grid regular
lattice. Our implementation of the SAR model is a variation of the
model found on page 406, Cressie, 1993, equation 6.3.8. Essentially,
we are decomposing the residuals of a simple trend model using
RESID[i] = SAR.ERROR[i] + WHITE.NOISE.ERROR[i]
The SAR.ERROR[i] terms each require a normal distribution prior in which
the mean is a function of the SAR.ERROR[j] terms of the nearest
neighbors. Our model is estimable because we have approximately 2400
data points with which to work.
Dr. Darren Wilkinson has already kindly pointed out a reference to
"Fast sampling of Gaussian Markov random fields",
Rue H., Journal of the Royal Statistical Society: Series B (Statistical
Methodology), 2001, vol. 63,
no. 2, pp. 325-338 (14) , Blackwell Publishers Ltd., Oxford, UK and Boston,
USA
as dealing with the issue of Bayesian estimation when there is high
dimensionality to the priors. (You may view his comments on the WinBUGS
listserv maintained at http://www.jiscmail.ac.uk/lists/BUGS.html.)
Has anyone else dealt with high dimensional parameter spaces in Bayesian
and/or Frequentist estimation? Additional references and comments would
be gratefully welcomed.
David Paul, Ph.D.
Battelle Memorial Institute
505 King Avenue
Columbus, OH 43201
614.424.3176
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