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The jewel of monte carlo methods is Markov Chain Monte Carlo (MCMC) for sampling from high-dimensional probability distributions. The math is more involved, but
by blt 8y ago
The jewel of monte carlo methods is Markov Chain Monte Carlo (MCMC) for sampling from high-dimensional probability distributions. The math is more involved, but the problem it solves is really hard and really important.
- tmalsburg2 8y agoWhile the math is complex, the algorithms are not necessarily. In its simplest form, MCMC sampling can be implemented in 10 lines of code (Metropolis-Hastings algorithm) -- an exercise that I recommend to everyone who's interested in the topic.
- blt 8y agoYeah I've noticed that pattern when I implement numerical algorithms by hand. A lot of the time they're pretty simple. But you need the analysis to be confident that it will work. A point in favor of formal CS / applied math :)
- theoh 8y agoThis is a good application: https://en.wikipedia.org/wiki/Metropolis_light_transport https://en.wikipedia.org/wiki/Metropolis_light_transport If anyone is looking for the "10 line" version of Metropolis, there's a tiny toy example in, for example, these SIGGRAPH course notes from 2001: http://cseweb.ucsd.edu/~viscomp/classes/cse274/wi18/readings/course29sig01.pdf http://cseweb.ucsd.edu/~viscomp/classes/cse274/wi18/readings...