SW {PottsUtils}

Generate Random Samples from a Compound Potts Model by the Swendsen-Wang Algorithm

Description

Generate random samples from a compound Potts model using the Swendsen-Wang algorithm.

Usage

  SW(n, nvertex, ncolor, edges, weights, beta)

Arguments

n

number of samples.

nvertex

number of vertices of a graph.

ncolor

number of colors each vertex can take.

edges

edges of a graph.

weights

weights of edges. One for each corresponding component in edges. The default values are 1s for all.

beta

the parameter inverse temperature of the Potts model.

Details

We use the Swendsen-Wang algorithm to generate random samples from a compound Potts model. See rPotts1 for more information on the compound Potts model.

Value

The output is a nvertex by n matrix with the kth column being the kth sample.

References

Robert H. Swendsen and Jian-Sheng Wang (1987) Nonuniversal Critical Dynamics in Monte Carlo Simulations Physical Review Letters vol. 58, no. 2, 86-88

Dai Feng (2008) Bayesian Hidden Markov Normal Mixture Models with Application to MRI Tissue Classification Ph. D. Dissertation, The University of Iowa

See Also

Wolff, BlocksGibbs

Examples

  #Example 1: Generate 100 samples from a Potts model with the
  #           neighborhood structure corresponding to a
  #           second-order Markov random field defined on a 
  #           3*3 2D graph. The number of colors is 2.
  #           beta=0.1. All weights are equal to 1.
 
  edges <- getEdges(mask=matrix(1, 2, 2), neiStruc=rep(2,4))
  set.seed(100)
  SW(n=500, nvertex=4, ncolor=2, edges, beta=0.8)