The basic idea is to apply Taylor's series approximation for the logarithm of the posterior pdf. In practise, the second order approximation is used. This amounts to approximating the posterior pdf by the Gaussian distribution.

Let us denote the posterior pdf by P(x). In practise the procedure is as follows:

- Find the maximum of -log P(x). Denote the maximum point by
x
_{0}. - Find the second order Taylor's series approximation of -log P(x)
around x
_{0}, i.e., compute the the Hessian matrix of -log P(x) at x_{0} - Normalise the approximated pdf so that it integrates to unity.

Back to the exercises.

Tästä sivusta vastaa Harri.Lappalainen@hut.fi.

Sivua on viimeksi päivitetty 4.2.1999.

URL: http://www.cis.hut.fi/cis/edu/Tik-61.181/laplace.html