The Living Thing / Notebooks :

Monte Carlo methods

Finding functionals (traditionally integrals) approximately by guessing cleverly. Often, but not always, used for approximate statistical inference, especially certain Bayesian techniques.

Or don't even guess randomly, but sample cleverly using the new shiny Quasi Monte Carlo.

See also compressed sensing, particle filters, and matrix concentration inequalities, and probably the most important use case, Bayesian statistics.

Markov chain samplers

See Markov Chain Monte Carlo.

Multi-level Monte Carlo

Hmmm. Also multi scale monte carlo, multi index monte carlo. See also uncertainty quantification.

mimclib is one possible tool here.