INFERENCES FROM THE POSTERIOR DENSITY

The posterior density function, Eq. (6.1-13), expresses all the information available about the postulated model from the data Y and the prior density function. Eq. (6.1-12). In this section we present some of the major results obtainable from this function. 

Let 6e denote the value of 6 on completion of the minimization of S 6). This solution corresponds to a mode (local maximum) of the posterior density p 6e Y). There will be just one mode if the model is linear in the parameters, but models nonlinear in 6 may have additional modes and one 

Once the principal mode is found, the posterior probability content of the adjoining region of 6 is computable (in principle) by numerical integration. This approach, however, is seldom feasible for multiparameter models. The needed integrals are expressible more concisely via the quadratic expansions 5 given in Eqs. (6.4-3) to (6.4-5), which are exact for models linear in e. 

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