Comment by xioxox
10 years ago
I'm a scientist who uses MCMC to sample the parameter space of a model and dataset, to get some idea of the uncertainties on the models parameters. These parameters are all continuous (albeit at the finite resolution of floating point numbers). Can someone from a CS background explain how this set approach connects to my idea of MCMC?
For any scientists, I'd heartily recommend emcee [1] as a sampler. This uses Goodman-Weare instead of Metropolis-Hastings, which works a lot better in practice, without having to figure out proposal distributions and so on.
This is something addressed by probability theory, not CS. While MCMC is easier to explain and understand for discrete spaces, it can also be used for continuous spaces. As a non-mathematician I just think about this as "discretizing at an infinitely high resolution", but of course to an actual mathematician/statistician this is nonsense.