With the ready availability of spatial databases and geographical information system software, statisticians are increasingly encountering multivariate modelling settings featuring associations of more than one type: spatial associations between data locations and associations between the...

type="main" xml:id="rssb12062-abs-0001"> <title type="main">Summary</title> <p>The essentials of our paper of 2002 are briefly summarized and compared with other criteria for model comparison. After some comments on the paper's reception and influence, we consider criticisms and proposals forimprovement made by us and others.

We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure "p"_"D" for the effective number of parameters in a model as the difference between the posterior mean of the...

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial...