### Useful Papers - Basic Statistical Modeling

**Primary**:

Friston et. al (1995), "Analysis of fMRI time-series revisited," NeuroImage 2, 45-53 PDF

Worsley & Friston (1995), "Analysis of fMRI time-series revisited - again," NeuroImage 2, 173-181 PDF

Summary: Friston et. al is the theoretical work extending the GLM to account for a known autocorrelation function, to enable the 'coloring' approach to noise autocorrelation in fMRI to be used. The authors argue that swamping unknown autocorrelation by temporally smoothing the data with a known kernel can produce less-biased parameter estimates than no correction. Worsley & Friston is essentialy a correction to the Friston et. al paper, fixing up some math issues.

Bottom line: Seemed like a good idea at the time, but the temporal smoothing approach to autocorrelation correction has been pretty discredited at this point for most fMRI work. This is useful historical background, though. Check out TemporalFilteringFaq for more details.

**Supplementary**:

Holmes et. al (1997), "Characterizing brain images with the general linear model," in: Frackowiak et. al (Eds.), Human Brain Function, San Diego: Academic Press, 59-84 PDF (or see Jeff for paper copies)

Summary: A ground-up description of the general linear model and how it's applied to neuroimaging data. Describes how the GLM works in good (but not too dense) mathematical detail, and how it's modified in the case of PET (and fMRI, to a shorter degree).

Bottom line: Actually an extremely helpful and quite intelligible description of the GLM as it's applied to neuroimaging. Very useful background on statistical analysis.

Bandettini et. al (1993), "Processing strategies for time-course data sets in functional MRI of the human brain," Magnetic Resonance in Medicine 30, 161-173 PDF (or see Jeff for paper copies)

Summary: Describes the physical and theoretical background for fMRI and a variety of different analysis pathways for dealing with data. One of the earliest papers to describe statistical analysis of fMRI data in thorough detail. Strategies described include voxel-by-voxel analysis, GLM methods, frequency domain methods, cross-correlation methods, and a number of others.

Bottom line: Historical background, more than anything. A good number of the strategies outlined here are pretty obsolete.