Metropolis Algorithm and Beyond
We have discussed in the previous chapters the important role of Monte Carlo methods in evaluating integrals and simulating stochastic systems. The most critical step in developing an efficient Monte Carlo algorithm is the simulation (sampling) from an appropriate probability distribution π(x). When directly generating independent samples from π(x) is not possible, we have to either opt for an importance sampling strategy, in which random samples are generated from a trial distribution different from (but close to) the target one and then weighted according to the importance ratio; or produce statistically dependent samples based on the idea of Markov chain Monte Carlo sampling.
KeywordsMarkov Chain Ising Model Transition Rule Detailed Balance Target Distribution
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