One common approach to analysing fMRI data is to consider each voxel separately within the framework of the general linear model.
The model assumes, at every time point, that the HDR is equal to the scaled and summed version of the events active at that point.
A researcher creates a design matrix specifying which events are active at any timepoint.
One common way is to create a matrix with one column per overlapping event, and one row per time point, and to mark it if a particular event, say a stimulus, is active at that time point.
One then assumes a specific shape for the HDR, leaving only its amplitude changeable in active voxels.
The design matrix and this shape are used to generate a prediction of the exact HDR response of the voxel at every timepoint, using the mathematical procedure of convolution.
This prediction does not include the scaling required for every event before summing them.

The basic model assumes the observed HDR is the predicted HDR scaled by the weights for each event and then added, with noise mixed in.
This generates a set of linear equations with more equations than unknowns.
A linear equation has an exact solution, under most conditions, when equations and unknowns match.
Hence one could choose any subset of the equations, with the number equal to the number of variables, and solve them.
But, when these solutions are plugged into the left-out equations, there will be a mismatch between the right and left sides, the error.
The GLM model attempts to find the scaling weights that minimize the sum of the squares of the error.
This method is provably optimal if the error were distributed as a bell curve, and if the scaling-and-summing model were accurate.
For a more mathematical description of the GLM model, see generalized linear models.

The GLM model does not take into account the contribution of relationships between multiple voxels.
Whereas GLM analysis methods assess whether a voxel or region's signal amplitude is higher or lower for one condition than another, newer statistical models such as multi-voxel pattern analysis (MVPA), utilize the unique contributions of multiple voxels within a voxel-population.
In a typical implementation, a classifier or more basic algorithm is trained to distinguish trials for different conditions within a subset of the data.
The trained model is then tested by predicting the conditions of the remaining (independent) data.
This approach is most typically achieved by training and testing on different scanner sessions or runs.
If the classifier is linear, then the training model is a set of weights used to scale the value in each voxel before summing them to generate a single number that determines the condition for each testing set trial.
More information on training and testing classifiers is at statistical classification.
One common approach to analysing fMRI data is to consider each voxel separately within the framework of the general linear model. The model assumes, at every time point, that the HDR is equal to the scaled and summed version of the events active at that point. A researcher creates a design matrix specifying which events are active at any timepoint. One common way is to create a matrix with one column per overlapping event, and one row per time point, and to mark it if a particular event, say a stimulus, is active at that time point. One then assumes a specific shape for the HDR, leaving only its amplitude changeable in active voxels. The design matrix and this shape are used to generate a prediction of the exact HDR response of the voxel at every timepoint, using the mathematical procedure of convolution. This prediction does not include the scaling required for every event before summing them.
The basic model assumes the observed HDR is the predicted HDR scaled by the weights for each event and then added, with noise mixed in. This generates a set of linear equations with more equations than unknowns. A linear equation has an exact solution, under most conditions, when equations and unknowns match. Hence one could choose any subset of the equations, with the number equal to the number of variables, and solve them. But, when these solutions are plugged into the left-out equations, there will be a mismatch between the right and left sides, the error. The GLM model attempts to find the scaling weights that minimize the sum of the squares of the error. This method is provably optimal if the error were distributed as a bell curve, and if the scaling-and-summing model were accurate. For a more mathematical description of the GLM model, see generalized linear models.
The GLM model does not take into account the contribution of relationships between multiple voxels. Whereas GLM analysis methods assess whether a voxel or region's signal amplitude is higher or lower for one condition than another, newer statistical models such as multi-voxel pattern analysis (MVPA), utilize the unique contributions of multiple voxels within a voxel-population. In a typical implementation, a classifier or more basic algorithm is trained to distinguish trials for different conditions within a subset of the data. The trained model is then tested by predicting the conditions of the remaining (independent) data. This approach is most typically achieved by training and testing on different scanner sessions or runs. If the classifier is linear, then the training model is a set of weights used to scale the value in each voxel before summing them to generate a single number that determines the condition for each testing set trial. More information on training and testing classifiers is at statistical classification.
Functional magnetic resonance imaging