Monte Carlo computation
Monte Carlo methods are simulation algorithms designed to compute answers to deterministic questions using random numbers. Although used in many branches of science, in statistics they are principally used to compute probabilities and expectations in complex stochastic models.
Markov chain Monte Carlo (MCMC) techniques are dynamic simulation methods where
variables are updated iteratively in a stationary way, and whose use in
computation depends on convergence theorems for Markov chains. These
methods have proved remarkably important in implementing Bayesian
Research in the group is focussed on several key areas of Monte Carlo methodology, including adaptive MCMC, particle filters, trans-dimensional MCMC and simulated annealing. It addresses both methodological issues (construction of algorithms) and theoretical aspects (proof of convergence, quantifying performance)
Monte Carlo methods were imported to the discipline of statistics from physics. In modern terms they originate from Los Alamos and the atomic bomb project, although there is reference to them as far back as the ancient Babylonians of Biblical times. Now they are applied across many scientific fields, including engineering, aerospace, image and speech recognition and robot navigation.
On the ergodicity properties of some adaptive MCMC algorithms (2006)
C. Andrieu and E. Moulines
Annals of Applied Probability, vol: 16, Issue: 3
Delayed rejection in reversible jump Metropolis-Hastings (2001)
Peter Green and Antonietta Mira
Biometrika, vol: 88, Pages: 1035 - 1053
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