One of the main challenges in fMRI studies is whole-brain activity and connectivity or modelling the 3-dimensional spatial dependence of imaging data. We proposed a novel 3-dimensional non-parametric Bayesian spatiotemporal model that allows to detect activated regions of brain and, simultaneously, functional connectivity by clustering of time series BOLD signals. In temporal dimension, we use long memory process with discrete wavelet transform on the error terms of model. Also, we model the data using a hemodynamic response function with a voxel-dependent parameter. We account for the 3-dimensional complex spatial correlation using Ising prior on activation indicators. In addition, functional connectivity is done by 3-dimensional clustering of the voxels’ time series. To achieve this goal, we imposed Dirichlet process on the long memory parameter. For posterior inference, we combine auxiliary variable method and also Neal’s algorithm 8 with Markov Chain Monte Carlo sampling approach. We investigate the properties of the proposed model through its performance on 3-dimensional simulated and real data sets.

Dirichlet process prior, discrete wavelet transform, long memory errors, Ising prior, fMRI.