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

## Multi-level Monte Carlo

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

mimclib is one possible tool here.

## Refs

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*ArXiv:1212.1377 [q-Fin]*. - GMRB12
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*ArXiv:1206.3255*. - HaNT16
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*ArXiv:1505.00965 [Physics, q-Fin, Stat]*. - KoCW15
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- Propp, J., & Wilson, D. (1998) Coupling from the Past: a User’s Guide.
- RuKr04
- Rubinstein, R. Y., & Kroese, D. P.(2004) The Cross-Entropy Method a Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning. . New York, NY: Springer New York
- RuKr08
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- RuRV14
- Rubinstein, R. Y., Ridder, A., & Vaisman, R. (2014) Fast sequential Monte Carlo methods for counting and optimization. . Hoboken, New Jersey: Wiley
- SiFT07
- Sisson, S. A., Fan, Y., & Tanaka, M. M.(2007) Sequential Monte Carlo without likelihoods.
*Proceedings of the National Academy of Sciences*, 104(6), 1760–1765. DOI. - Xia11
- Xia, Y. (2011) Multilevel Monte Carlo method for jump-diffusion SDEs.
*ArXiv:1106.4730 [q-Fin]*.