MRIaggr (version 1.1.5)

rhoMF: Estimation of the local and regional spatial correlation

Description

Estimation the spatial regularization parameters on external data using mean field approximation.

Usage

rhoMF(Y, W_SR, rho_max = 50, prior_prevalence = TRUE,  test.regional = FALSE, W_LR, distance.ref, coords, threshold = 0.1,
	nbGroup_min = 100, regionalGroups = "last_vs_others", multiV = TRUE)

Arguments

Y

a matrix containing the observations (by rows) for the various groups (by columns). REQUIRED.

W_SR

the local neighbourhood matrix. dgCMatrix. Should be normalized by row (i.e. rowSums(Wweight_SR)=1). REQUIRED.

rho_max

Maximum possible rho value (numeric), minimum is 0.

prior_prevalence

should a prior on class prevalence be including when estimating the regularisation parameters ? logical.

test.regional

Should regional regularization be considered. logical.

W_LR

the regional neighbourhood matrix. dgCMatrix. Should be contains the distances between the observations (0 indicating infinite distance).

distance.ref

the interval of distance defining the several neighbourhood orders in W_LR. numeric vector.

threshold

the minimum value of the posterior probability for group G for being considered as lesioned when forming the spatial groups. double.

nbGroup_min

the minimum group size of the spatial groups required for computing the regional potential. integer.

coords

coordinates of each site. matrix.

regionalGroups

how should the regional potential be computed : last group versus the others ("last_vs_others") or for each group ("each").

multiV

should the regional neighbourhood range be computed for each spatial group ? logical.

Value

A numericVector containing the estimated regularisation parameter(s).

See Also

calcW to compute the neighbourhood matrix, simulPotts to draw simulations from a Potts model. rhoLvfree to estimate the regularization parameters using mean field approximation. calcPottsParameter general interface for estimating the regularization parameters.

Examples

# spatial field
## Not run: 
# n <- 50
# ## End(Not run)

G <- 3
coords <- which(matrix(0, nrow = n * G, ncol = n * G) == 0,arr.ind = TRUE)

# neighbourhood matrix
W_SR <- calcW(as.data.frame(coords), range = sqrt(2), row.norm = TRUE)$W
W_LR <- calcW(as.data.frame(coords), range = 10, row.norm = FALSE)$W

# initialisation
set.seed(10)
sample <- simulPotts(W_SR, G = 3, rho = 3.5, iter_max = 500, 
                     site_order = TRUE)$simulation

multiplot(as.data.frame(coords), sample,palette = "rgb")

# estimation
rho <- rhoMF(Y=sample, W_SR = W_SR)
rho

# the regional potential is computed for each group
rho <- rhoMF(Y = sample, W_SR = W_SR,
             test.regional = TRUE, W_LR = W_LR, distance.ref = seq(1, 10, 0.5),
			 coords = coords, regionalGroups = "each")
rho

# the regional potential is computed for the last group vs. the others
rho <- rhoMF(Y = sample, W_SR = W_SR,
             test.regional = TRUE, W_LR = W_LR, distance.ref = seq(1, 10, 0.5),
			 coords = coords, regionalGroups = "last_vs_others")
rho