A note on marginal likelihood for Gaussian models
نویسنده
چکیده
For a vector y ∈ Rn and a model subspace X ⊂ Rn, the residual configuration statistic is what remains of y when translations in the model space and scalar multiplication are ignored. The configuration statistic for a linear Gaussian model has a distribution that depends only on variance-component ratios, or similar ratio parameters in the covariance function of a spatial model. The marginal likelihood based on the configuration statistic is derived analytically. Ordinarily, if the number of nuisance parameters is not too large, the profile likelihood is approximately equal to the marginal likelihood when both are well defined. But it is extremely unusual for these to be identical. The residual configuration statistic is one such example, in which the marginal likelihood coincides with Diggle’s (1988) hybrid profile REML likelihood.
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