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Applied Bayesian Modelling, 2nd Edition by Peter Congdon

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The relation between c08-math-0593 and c08-math-0594 may be modelled over distance bands (e.g. vianon-linear regression) involving parametric forms such as above.

However, there are drawbacks to such procedures (Diggle and Ribeiro, 2002), and Bayesian approaches to spatial covariance generally focus on likelihood based estimation and interpolation (Ecker and Gelfand, 1997). For the linear model

equation

with covariance

equation

the log-likelihood kernel is

equation

Identifiability of parameters may be improved (and sampling reduced) by discrete priors for the range parameter c08-math-0598, or on the nugget to sill ratio c08-math-0599 in the reparameterized covariance matrix (Diggle and Ribeiro, 2007, Chapter 7; Diggle et al., 2003, p. 65). Modifications of this likelihood ...

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