"Instead of attempting to use direct numerical integration techniques, stochastic sampling techniques or Monte Carlo integration is an alternative. As mentioned, the key idea embedded in the MC approach is to represent the required distribution as a set of random samples rather than a specific analytic function (e.g., Gaussian). As the number of samples becomes large, they provide an equivalent (empirical) representation of the distribution enabling moments to be estimated directly (inference)."

Bayesian Signal Processing, James V. Candy, 2009