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I doing spatial bayesian data analysis, I am assuming a no-nugget exponential covariance. I have tried a variety of priors for the sills and range parameters (gamma, inverse gamma etc.) , unfortunately the convergence diagonstics are typically horrible.

I am wondering how to figure out the poor mixing I observe, is there something I can do to make the MCMC chain behave better?

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Diggle and Ribeiro discuss this in their book ("Model-based Geostatistics"): see section 5.4.2. They quote some research suggesting that re-parameterization might help a little. For an exponential model (a Matern model with kappa = 1/2) this research suggests using the equivalent of log(sill/range) and log(range). Diggle and Ribeiro themselves recommend a profile likelihood method to investigate the log-likelihood surface. Their software is implemented in the R package geoRglm.

Have you looked at an experimental variogram to check that a zero nugget and an exponential shape are appropriate?

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  • $\begingroup$ Thanks. I fitted a no nugget model to the likelihood using proc mixed, I guess I should compare the AICC with that of a model with nugget. $\endgroup$ – Arin Chaudhuri Aug 19 '10 at 18:08
  • $\begingroup$ I would agree with whuber though that the visualization of the variogram cloud would be really helpful in determining if you choice of model seems appropriate. $\endgroup$ – TheSteve0 Nov 28 '10 at 7:51

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