21.5 A posteriori Bayes estimators for regression parameters

In case one wants to have point estimates for the regression parameters θ1,…,θk this is possible by using the marginal distributions of the individual parameters. Let πj(·) be the marginal distribution of j calculated from the a posteriori density π(·|D), then the a posteriori Bayes estimator for θj is the expectation of j˜, i.e.

The a posteriori Bayes estimator for the parameter vector θ = (θ1,…,θk) is given by

Remark 21.1:

Another possibility for point estimates for the θj would be the median of the marginal distribution of j.

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