The quadratic approximation, also known as the Laplace method or the normal approximation, consists of approximating the posterior, 
, with a Gaussian distribution, 
.
This method consists of two steps:
- Find the mode of the posterior distribution. This will be the mean of
. - Compute the Hessian matrix. From this, we can compute the standard deviation of .
The first step can be done numerically using optimization methods, that is, ...
