The goal of an fMRI data analysis is to analyze each voxel's time series to see whether the BOLD signal changes in response to some manipulation. For example, if a stimulus was repeatedly presented to a subject in a blocked fashion, following the trend shown in the red line in the top panel of Figure 5.1, we would search for voxel time series that match this pattern, such as the BOLD signal shown in blue. The tool used to fit and detect this variation is the general linear model (GLM), where the BOLD time series plays the role of dependent variable, and the independent variables in the model reflect the expected BOLD stimulus timecourses. Observe, though, that square wave predictor in red doesn't follow the BOLD data very well, due to sluggish response of the physiology. This leads to one major focus of this chapter: Using our understanding of the BOLD response to create GLM predictors that will model the BOLD signal as accurately as possible. The other focus is modeling and accounting for BOLD noise and other souces of variation in fMRI time series.

Throughout this chapter the models being discussed will refer to modeling the BOLD signal in a single voxel in the brain. Such a voxel-by-voxel approach is known as a mass univariate data analysis, in contrast to a multivariate approach (see Chapters 8 and 9 for uses of multivariate models).