Assessing Dynamic Effects on a Bayesian Matrix-Variate Dynamic Linear Model: an Application to fMRI Data Analysis

In this work, we propose a modeling procedure for fMRI data analysis using a Bayesian Matrix-Variate Dynamic Linear Model (MVDLM). With this type of model, less complex than the more traditional temporal-spatial models, we are able to take into account the temporal and -- at least locally -- the spatial structures that are usually present in this type of data. Despite employing a voxel-wise approach, every voxel in the brain is jointly modeled with its nearest neighbors, which are defined through a euclidian metric. MVDLM's have been widely used in applications where the interest lies in to perform predictions and/or analysis of covariance structures among time series. In this context, our interest is rather to assess the dynamic effects which are related to voxel activation. In order to do so, we develop three algorithms to simulate online-trajectories related to the state parameter and with those curves or simulated trajectories we compute a Monte Carlo evidence for voxel activation. Through two practical examples and two different types of assessments, we show that our method can be viewed for the practitioners as a reliable tool for fMRI data analysis. Despite all the examples and analysis are illustrated just for a single subject analysis, we also describe how more general group analysis can be implemented.