Changing Dimension
The reversible-jump method is a variant of Metropolis–Hastings that allows proposals that change the dimensionality of the space. This method was proposed in 1995 by Peter Green of Bristol University. Markov chain Monte Carlo methods that change dimensionality have also long been used in statistical physics applications, where for some problems a distribution that is a grand canonical ensemble is used (e.g., when the number of molecules in a box is variable). Some sort of reversible-jump variant is also needed when doing MCMC or Gibbs sampling over nonparametric Bayesian models such as those involving the Dirichlet process or Chinese restaurant process, where the number of mixing components/clusters/etc. is automatically inferred from the data.
Read more about this topic: Markov Chain Monte Carlo
Famous quotes containing the words changing and/or dimension:
“A culture may be conceived as a network of beliefs and purposes in which any string in the net pulls and is pulled by the others, thus perpetually changing the configuration of the whole. If the cultural element called morals takes on a new shape, we must ask what other strings have pulled it out of line. It cannot be one solitary string, nor even the strings nearby, for the network is three-dimensional at least.”
—Jacques Barzun (b. 1907)
“Le Corbusier was the sort of relentlessly rational intellectual that only France loves wholeheartedly, the logician who flies higher and higher in ever-decreasing circles until, with one last, utterly inevitable induction, he disappears up his own fundamental aperture and emerges in the fourth dimension as a needle-thin umber bird.”
—Tom Wolfe (b. 1931)