NC.mrf: Normalising constant of a Gibbs Random Field

In GiRaF: Gibbs Random Fields Analysis

Description

Partition function 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 25 for 2-state models).

Usage

NC.mrf(h, w, param, ncolors = 2, nei = 4,  
       pot = NULL, top = NULL, left = NULL, 
       bottom = NULL, right = NULL, corner = NULL)

Arguments

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.

References

Friel, N. and Rue, H. (2007). Recursive computing and simulation-free inference for general factorizable models. Biometrika, 94(3):661–672.

Reeves, R. and Pettitt, A. N. (2004). Efficient recursions for general factorisable models. Biometrika, 91(3):751–757.

See Also

The “GiRaF-introduction” vignette

Examples

# 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)

GiRaF documentation built on Oct. 23, 2020, 6:07 p.m.