sim.adaptiveGMRF2COVAR {adaptsmoFMRI}

Adaptive GMRF Model for Simulated Data

Description

This function estimates the effects of a synthetic spatiotemporal data set resembling functional MR Images (fMRI), with the method of efficient Markov Chain Monte Carlo (MCMC) simulation. The Metropolis Hastings (MH) algorithm is used for the non-approximate case and the Gibbs sampler for the approximate case.

Usage

  sim.adaptiveGMRF2COVAR(data, hrf, approximate = FALSE, K
    = 500, a = 1, b = 1, c = 1, d = 1, nu = 1, block = 1,
    burnin = 1, thin = 1)

Arguments

data

simulated fMRI-data, needs to be an array of dimension (20 x 20 x T).

hrf

haemodynamic response function, needs to be a vector of length T.

approximate

logical, if TRUE then the approximate case is chosen. Default is FALSE.

K

scalar, length of the MCMC path, hence iteration steps.

a

scalar, shape hyperparameter of the inverse-gamma distribution of the variance parameter (\sigma_i^2).

b

scalar, scale hyperparameter of the inverse gamma distribution of the variance parameter (\sigma_i^2).

c

scalar, shape hyperparameter of the inverse gamma distribution of the precision parameter (\tau).

d

scalar, scale hyperparameter of the inverse gamma distribution of the precision parameter (\tau).

nu

scalar, shape and scale hyperparameter of the gamma distribution of the interaction weights (w_{ij}).

block

scalar, when approximate==TRUE then a block of weights is updated at a time.

burnin

scalar, defining the first iteration steps which should be omitted from MCMC path.

thin

scalar, only every thin step of MCMC path is saved to output.

Value

dx

scalar, number of pixels in x-direction.

dy

scalar, number of pixels in y-direction.

I

scalar, number of pixels.

iter

scalar, number of MCMC iterations.

coord

matrix, coordinates of pixels.

nei

matrix, locations of weights in precision matrix.

NEI

scalar, number of weights.

beta.out

matrix, MCMC path of covariates.

w.out

matrix, MCMC path of weights.

sigma.out

matrix, MCMC path of variance parameters.

tauk.out

matrix, MCMC path of hyper parameters.

Note

This function is solely for two covariates.

Author(s)

Maximilian Hughes

Examples

# See example function for simulated data (one covariate).