# Adaptive GMRF Model for Simulated Data 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. ```r sim.adaptiveGMRF(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. ## Note This function is solely for one covariate. ## Examples ```r # non-transformed hr-function T <- 210 seq.length <- T*3 index <- seq(3, T*3, by = 3) hrf <- rep(c(-0.5, 0.5), each=30, times=ceiling(T/30*1.5)) hrf <- as.matrix(hrf[index]) # get simulated data data("sim_fmri") data <- data_simfmri # execute function set.seed(111222) K <- 2 a <- b <- c <- d <- nu <- 1 test.sim.adaptive <- sim.adaptiveGMRF(data, hrf, approximate=TRUE, K, a, b, c, d, nu) ``` ## Returns - **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. ## Author(s) Maximilian Hughes

sim.adaptiveGMRF function