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

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  • Monica Palaseanu-Lovejoy
    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 7:17 AM
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      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
      Oxford Road
      Manchester M13 9PL
      England, UK
      Tel: +44 (0) 275 8689
      Email: monica.palaseanu-lovejoy@...
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