## RE: [ai-geostats] Bayesian kriging(s)?

Expand Messages
• Hi, Well, the bayesian kriging methods you are describing are somewhat different than what i am using. I am using R and geoR by Ribeiro and Diggle (2001). Web
Message 1 of 10 , Aug 31, 2004
• 0 Attachment
Hi,

Well, the bayesian kriging methods you are describing are
somewhat different than what i am using. I am using R and geoR
by Ribeiro and Diggle (2001).

Web pages for R:{ HYPERLINK "http://cran.r-project.org/" }http://cran.r-project.org/

Web page for geoR: www.est.ufpr.br/geoR

Usually with Bayesian kriging you will have higher variance just
because the uncertainty is incorporated in all (some) parameters,
while for the geostatistical kriging (or the "other kriging") there is no
uncertainty assumed for the semi-variogram model. So, in a way
kriging is a particular case of bayesian kriging as it is described by
Ribeiro and Diggle.

Uncertainty can be assumed for nugget, variance, mean and range,
or only for one parameter, or a combination of parameters. Usually
everything is depending on how well one is understanding the data,
or at least so i think. Citing from Ribeiro the inference is done by
Monte Carlo simulations, and samples are taken from the posterior
and predictive distributions and used for inference and predictions.
One of his algorithms looks like that:

1. Choose a range of values for phi (range parameter in
geostatistical kriging) which is sensible for the given data, and
assign a discrete uniform prior for phi on a set of values spanning
the chosen range;

2. compute the posterior probabilities on this discrete support set,
defining a discrete posterior distribution with probability mass
function pr(phi | y);

3. sample a value of phi from this discrete distribution pr(phi | y);

4. attach the sampled value phi to the distribution [beta, sigma
square |y, phi] and sample from this distribution (beta = mean
param., sigma square = variance, phi = range)

5. repeat steps 3 and 4 as many times as required / desired. the
resulting sample of the triplets (beta, sigma square, phi) is a
sample from the joint posterior distribution.

In my experience, if the data set is highly skewed and the spatial
autocorrelation is weak, bayesian kriging does a better job than
geostatistical kriging, even if the data is transformed to approach
normality. From literature (see the paper mentioned by Edzer
Pebesma - Moyeed and Papritz, Math Geol 34(4), 365-386) it
seems that for very large sets of data (n > 2500) the advantage
Bayesian kriging has over geostatistical kriging is minimal, while
with the data sets i am using (random locations, weak spatial
autocorrelation, areas of spatial heterogeneity, n in between 200 to
350 points), Bayesian kriging seems to be superior.

I hope this helps a little,

Monica

Monica Palaseanu-Lovejoy
University of Manchester
School of Geography
Mansfield Cooper Bld. 3.21