Computing
MAP estimates can be computed in several ways:
- Analytically, when the mode(s) of the posterior distribution can be given in closed form. This is the case when conjugate priors are used.
- Via numerical optimization such as the conjugate gradient method or Newton's method. This usually requires first or second derivatives, which have to be evaluated analytically or numerically.
- Via a modification of an expectation-maximization algorithm. This does not require derivatives of the posterior density.
- Via a Monte Carlo method using simulated annealing
Read more about this topic: Maximum A Posteriori Estimation