Inferences for Predicted Functions

Frequently one wants to analyze the posterior density of some result calculated from a fitted model. Such information is obtainable by a transformation of the posterior density, as outlined below and illustrated in Example C.2 of Appendix C. This analysis parallels that of Clarke (1987). 

First-order Taylor expansions of the auxiliary functions around Og and (t give 

The parametric inferences in Section 6.6.1 can now be taken over directly. One simply replaces A by and elements of 6g by corresponding elements of 0. Thus, Eqs. (6.6-7) and (6.6-8) give the covariance matrix 

A vector 0 oi na P functions can also be treated, noting that Eq. (6.6-16) needs only the corresponding rows of J. Let 

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