Description Usage Arguments References See Also Examples
exact.mrf gives exact 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 and a small number of rows (up to 19 for 2-state models).
1 2 3 |
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. |
view |
Logical value indicating whether the draw should be printed. Do not display the optional borders. |
Friel, N. and Rue, H. (2007). Recursive computing and simulation-free inference for general factorizable models. Biometrika, 94(3):661–672.
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 | # 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)
# 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)
|
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 1 1 1 1 1 1 1 1 0 0
[2,] 1 1 0 0 1 0 1 1 0 0
[3,] 1 1 1 0 0 0 0 1 0 0
[4,] 1 1 1 1 1 0 1 0 0 1
[5,] 1 1 1 1 1 1 1 0 0 0
[6,] 1 1 1 1 1 0 0 1 0 1
[7,] 1 1 1 1 1 0 0 1 1 1
[8,] 1 1 1 1 0 1 0 0 1 0
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 0 1 1 1 1 1 1 1 1 0
[2,] 1 1 1 1 0 1 1 1 0 0
[3,] 1 1 1 0 0 1 1 1 0 1
[4,] 0 1 1 0 0 1 1 1 0 1
[5,] 0 0 0 0 0 0 0 0 0 1
[6,] 1 0 1 0 0 0 0 1 1 1
[7,] 1 0 0 0 0 0 0 1 1 1
[8,] 0 0 1 1 1 1 0 0 0 1
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 1 1 1 1 1 1 1 1 0 0
[2,] 0 1 0 1 0 1 0 0 1 0
[3,] 1 1 0 1 1 1 1 1 0 1
[4,] 0 1 1 1 1 1 1 1 1 1
[5,] 0 0 0 1 0 0 0 0 1 1
[6,] 0 0 0 0 0 0 0 1 1 0
[7,] 1 1 1 1 0 0 0 1 1 0
[8,] 1 1 1 0 0 0 0 1 0 0
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 0 1 1 1 1 1 1 1 1 1
[2,] 0 0 1 1 1 0 1 1 1 1
[3,] 0 0 0 0 0 1 1 1 1 1
[4,] 0 0 0 0 0 1 1 0 0 0
[5,] 0 1 0 0 0 1 1 0 0 0
[6,] 0 0 0 0 1 0 0 0 0 0
[7,] 0 0 0 1 1 0 0 0 1 1
[8,] 1 1 1 1 1 1 0 1 1 0
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