Description Usage Arguments References See Also Examples
sampler.mrf gives approximate sample from the likelihood of a general Potts model defined on a rectangular h x w lattice (h ≤ 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)).
1 2 3 4 |
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. |
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.
The “GiRaF-introduction” vignette
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | # 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)
|
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[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
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[66,] 1 1 1 1 1 1 1 1 1 1 1 1
[67,] 1 1 1 1 1 1 1 1 1 1 1 0
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[,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
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[23,] 1 1 1 1 1 1 1 1 1 1 1 0
[24,] 1 1 1 1 1 1 1 1 0 1 1 1
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[60,] 1 0 1 1 0 0 1 1 0 1 1 1
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[63,] 0 1 0 1 1 1 1 1 0 0 0 0
[64,] 0 1 1 1 1 1 0 0 0 1 1 0
[65,] 1 1 1 0 0 0 0 0 0 1 0 1
[66,] 1 1 1 1 1 1 0 0 0 1 1 1
[67,] 1 1 1 1 1 1 1 0 0 0 1 0
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[69,] 1 1 1 1 1 1 1 1 0 1 1 1
[70,] 1 1 1 1 1 1 0 1 1 1 1 1
[71,] 1 1 1 1 1 1 1 1 1 1 1 1
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[100,] 1 0 0 0 1 1 0 1 1 0 1 1
[,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
[1,] 0 0 1 1 1 1 1 1 0 0 0 1
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[,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61]
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[40,] 1 1 1 1 1 0 1 1 1 1 1 1
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