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##

Gaussian approximation of the posterior distribution

The substance of the results seen in the previous section
holds also in the case in which the prior is not flat and, hence,
cannot be absorbed in the normalization constant of the posterior.
In fact, in many practical cases the posterior exhibits an approximately
(multi-variate) Gaussian shape, even if the prior was not trivial.
Having at hand an *un-normalized* posterior , i.e.

we can take its *minus-log* function
.
If
has
approximately a Gaussian shape, it follows that

can be evaluated as

where
was obtained from the
minimum of
.

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Giulio D'Agostini
2003-05-13