GiRaF-package {GiRaF} | R Documentation |
GiRaF is a package for calculations on, and sampling from Gibbs (or discrete Markov) random fields.
GiRaF offers various tools for the analysis of Gibbs random fields and more precisely general homogeneous Potts model with possible anisotropy and potential on singletons (cliques composed of single vertex). GiRaF substantially lowers the barrier for practitioners aiming at analysing such Gibbs random fields. GiRaF contains exact methods for small lattices and several approximate methods for larger lattices that make the analysis easier for practitioners.
The “GiRaF-introduction” vignette gives a detailled introduction on the package.
For a complete list of functions, use library(help = "GiRaF").
Julien Stoehr, Pierre Pudlo and Nial Friel.
Maintainer: Julien Stoehr <julien.stoehr@ucd.ie>
Friel, N. and Rue, H. (2007). Recursive computing and simulation-free inference for general factorizable models. Biometrika, 94(3):661–672.
Geman, S. and Geman, D. (1984). Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intellignence, 6(6):721-741.
Reeves, R. and Pettitt, A. N. (2004). Efficient recursions for general factorisable models. Biometrika, 91(3):751–757.
Swendsen, R. H. and Wang, J.-S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Pysical Review Letters, 58(2):86-88.
The “GiRaF-introduction” vignette
# Dimension of the lattice height <- 8 width <- 10 # Interaction parameter Beta <- 0.6 # Isotropic configuration # Beta <- c(0.6, 0.6) # Anisotropic configuration when nei = 4 # Beta <- c(0.6, 0.6, 0.6, 0.6) # Anisotropic configuration when nei = 8 # Number of colors K <- 2 # Number of neighbors G <- 4 # Optional potential on sites potential <- runif(K,-1,1) # Optional borders. Top <- Bottom <- sample(0:(K-1), width, replace = TRUE) Left <- Right <- sample(0:(K-1), height, replace = TRUE) Corner <- sample(0:(K-1), 4, replace = TRUE) # Partition function for the default setting NC.mrf(h = height, w = width, param = Beta) # When specifying the number of colors and neighbors NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta) # When specifying an optional potential on sites NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta, pot = potential) # When specifying possible borders. The users will omit to mention all # the non-existing borders NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta, top = Top, left = Left, bottom = Bottom, right = Right, corner = Corner) # Exact sampling for the default setting exact.mrf(h = height, w = width, param = Beta, view = TRUE) # When specifying the number of colors and neighbors exact.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta, view = TRUE) # When specifying an optional potential on sites exact.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta, pot = potential, view = TRUE) # When specifying possible borders. The users will omit to mention all # the non-existing borders exact.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta, top = Top, left = Left, bottom = Bottom, right = Right, corner = Corner, view = TRUE) # Algorithm settings n <- 200 method <- "Gibbs" # Sampling method for the default setting sampler.mrf(iter = n, sampler = method, h = height, w = width, param = Beta, view = TRUE) # Sampling using an existing configuration as starting point sampler.mrf(iter = n, sampler = method, h = height, w = width, ncolors = K, nei = G, param = Beta, initialise = FALSE, view = TRUE) # Specifying optional arguments. The users may omit to mention all # the non-existing borders sampler.mrf(iter = n, sampler = method, h = height, w = width, ncolors = K, nei = G, param = Beta, pot = potential, top = Top, left = Left, bottom = Bottom, right = Right, corner = Corner, view = TRUE) # Gibbs sampler with sequential updates of the sites. sampler.mrf(iter = n, sampler = "Gibbs", h = height, w = width, ncolors = K, nei = G, param = Beta, random = FALSE, view = TRUE)