Classical and Bayesian Inference in fMRI - Advance Image Processing in Magnetic Resonance Imaging - page 538

parameters are estimated more efficiently and stimuli can be presented at any
point in the interstimulus interval. The latter is important because time locking
stimulus presentation and data acquisition gives a biased sampling over peris-
timulus time and can lead to differential sensitivities in multislice acquisition
over the brain.

17.4 STATISTICAL PARAMETRIC MAPPING

Statistical parametric mapping (SPM) entails the construction of spatially
extended statistical processes to test hypotheses about regionally specific effects
(21). SPMs are image processes with voxel values that are, under the null hypoth-
esis, distributed according to a known probability density function, usually the
Student's t - or f - distributions. These are known colloquially as t - or f -maps. The
success of statistical parametric mapping is due largely to the simplicity of the idea.
One analyzes each and every voxel using any standard (univariate) statistical test.
The resulting statistical parameters are assembled into an image — the SPM.
SPMs are interpreted as spatially extended statistical processes by referring to
the probabilistic behavior of Gaussian fields (22-25). GRF model both the univari-
ate probabilistic characteristics of a SPM and any nonstationary spatial covariance
structure. “Unlikely” excursions of the SPM are interpreted as regionally specific
effects, attributable to the sensorimotor or cognitive process that has been manip-
ulated experimentally.
Over the years, statistical parametric mapping has come to refer to the con-
joint use of GLM and GRF theory to analyze and make classical inferences about
spatially extended data through SPMs. The GLM is used to estimate some param-
eters that could explain the spatially continuous data in exactly the same way as
in conventional analysis of discrete data. GRF theory is used to resolve the
multiple comparison problem that ensues when making inferences over a volume
of the brain. GRF theory provides a method for correcting p values for the search
volume of an SPM and plays the same role for continuous data (i.e., images) as
the Bonferroni correction for the number of discontinuous or discrete statistical
tests. The approach was called SPM for three reasons: (1) to acknowledge “sig-
nificance probability mapping”, the use of interpolated pseudomaps of p values
used to summarize the analysis of multichannel ERP studies; (2) for consistency
with the nomenclature of parametric maps of physiological or physical parameters
(e.g., regional cerebral blood flow rCBF or volume rCBV parametric maps); and
(3) In reference to the parametric statistics that comprise the maps. Despite its
simplicity, there are some fairly subtle motivations for the approach that deserve
mention. Usually, given a response or dependent variable comprising many thou-
sands of voxels, one would use multivariate analyses as opposed to the mass-
univariate approach that SPM represents. The problems with multivariate
approaches are they do not support inferences about regionally specific effects,
they require more observations than the dimension of the response variable (i.e.,
number of voxels) and even in the context of dimension reduction, they are less
sensitive to focal effects than mass-univariate approaches. A heuristic argument