sampler.mrf {GiRaF}

MCMC samplers for Gibbs Random Fields

Description

sampler.mrf gives approximate sample from the likelihood of a general Potts model defined on a rectangular h x w lattice (h \le w) with either a first order or a second order dependency structure. Available options are the Gibbs sampler (Geman and Geman (1984)) and the Swendsen-Wang algorithm (Swendsen and Wang (1987)).

Usage

sampler.mrf(iter, sampler = "Gibbs" , h, w, 
          param, ncolors = 2, nei = 4, pot = NULL, 
          top = NULL, left = NULL, bottom = NULL, right = NULL, 
          corner = NULL, initialise = TRUE, random = TRUE, view = FALSE)

Arguments

iter

Number of iterations of the algorithm.

sampler

The method to be used. The latter must be one of "Gibbs" or "SW" corresponding respectively to the Gibbs sampler and the Swendsen-Wang algorithm.

h

the number of rows of the rectangular lattice.

w

the number of columns of the rectangular lattice.

param

numeric entry setting the interaction parameter (edges parameter)

ncolors

the number of states for the discrete random variables. By default, ncolors = 2.

nei

the number of neighbors. The latter must be one of nei = 4 or nei = 8, which respectively correspond to a first order and a second order dependency structure. By default, nei = 4.

pot

numeric entry setting homogeneous potential on singletons (vertices parameter). By default, pot = NULL

top, left, bottom, right, corner

numeric entry setting constant borders for the lattice. By default, top = NULL, left = NULL, bottom = NULL, right = NULL, corner = NULL.

initialise

Logical value indicating whether initial guess should be randomly drawn.

random

Logical value indicating whether the sites should be updated sequentially or randomdly. Used only with the "Gibbs" option.

view

Logical value indicating whether the draw should be printed. Do not display the optional borders.

References

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.

Swendsen, R. H. and Wang, J.-S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Pysical Review Letters, 58(2):86-88.

See Also

The “GiRaF-introduction” vignette

Examples

# Algorithm settings
n <- 200
method <- "Gibbs"

# Dimension of the lattice
height <- width <- 100

# 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)

# 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)