Monte Carlo Methods

MCMC

Wikipedia article on MCMC

Some important recipes:

Adaptive MCMC

This refers to MCMC methods that tries to learn sequentially from past simulations so as to adapt either (a) some aspects of the Markov kernel (e.g. the proposal mechanism in a Metropolis kernel), or (b) the invariant distribution; an example of the latter is the Wang-Landau algorithm. Andrieu and Thoms (pdf) (2008) is a nice tutorial on Adaptive MCMC, with focus on (a). A review of methods related to (b) that originates mostly from Physics may be found in Chopin et al. (ArXiv) (2011)

Sequential MC

Wikipedia article on Sequential MC/Particle filter

ABC (Approximate Bayesian Computation)

Nice introductions to ABC include a general introduction by Marin et al. (2011), Approximate Bayesian Computational methods (ArXiv). Another introduction, with a stronger focus on applications in Ecology and population genetics: Beaumont (2010), Approximate Bayesian computation in evolution and ecology (pdf). See also the web page of the DIY-ABC package.

Nicolas Chopin

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