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Are there any Lot-Of-Math Introduction to Monte Carlo Methods?
by hackandtrip 8y ago
Are there any Lot-Of-Math Introduction to Monte Carlo Methods?
- theoh 8y agoI'm not sure, since it doesn't introduce the notion of detailed balance, whether this article really deals meaningfully with the use of Markov chains at all. It doesn't bring out the fact that the Markov chain transition probabilities have to be tuned to explore the parameter space. The relative efficiency of MCMC versus a naive random sampling approach depends on this leveraging of detailed balance so that the correlations of the Markov chain work in favour of the experiment. So given that the article introduces this notion of a random walk, so it seems like it's going to discuss the Metropolis algorithm, it's not great that it ducks the main issue which is why a correlated Markov chain random walk is a useful approach. The key is that it's a "conditioned" random walk, and the method by which it is conditioned is the real trick to MCMC (at least to Metropolis, which is the cool kind.)