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

Oxford Road

Manchester M13 9PL

England, UK

Tel: +44 (0) 275 8689

Email: monica.palaseanu-lovejoy@...