swNoData {bayesImageS}

Simulate pixel labels using the Swendsen-Wang algorithm.

Description

The algorithm of Swendsen & Wang (1987) forms clusters of neighbouring pixels, then updates all of the labels within a cluster to the same value. When simulating from the prior, such as a Potts model without an external field, this algorithm is very efficient.

Usage

swNoData(beta, k, neighbors, blocks, niter = 1000, random = TRUE)

Arguments

beta

The inverse temperature parameter of the Potts model.

k

The number of unique labels.

neighbors

A matrix of all neighbors in the lattice, one row per pixel.

blocks

A list of pixel indices, dividing the lattice into independent blocks.

niter

The number of iterations of the algorithm to perform.

random

Whether to initialize the labels using random or deterministic starting values.

Value

A list containing the following elements:

alloc

An n by k matrix containing the number of times that pixel i was allocated to label j.

z

An (n+1) by k matrix containing the final sample from the Potts model after niter iterations of Swendsen-Wang.

sum

An niter by 1 matrix containing the sum of like neighbors, i.e. the sufficient statistic of the Potts model, at each iteration.

References

Swendsen, R. H. & Wang, J.-S. (1987) "Nonuniversal critical dynamics in Monte Carlo simulations" Physical Review Letters 58(2), 86–88, DOI: doi: 10.1103/PhysRevLett.58.86

Examples

# Swendsen-Wang for a 2x2 lattice
neigh <- matrix(c(5,2,5,3,  1,5,5,4,  5,4,1,5,  3,5,2,5), nrow=4, ncol=4, byrow=TRUE)
blocks <- list(c(1,4), c(2,3))
res.sw <- swNoData(0.7, 3, neigh, blocks, niter=200)
res.sw$z
res.sw$sum[200]