Description Usage Arguments References See Also Examples

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).

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. |

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.

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 | ```
# 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)
``` |

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