–25–
Mathematics and Implementation
¥ Available in PDF (scanned from hand-written pages) for the truly devoted
H File 3dREMLfit_mathnotes.pdf
¥ Outline of REML estimation methodology
H What is REML and why do we care?
¥ Matrix algebra for efficient solution of the many linear systems that must be solved for each voxel
H Sparse matrix factorizations, multiplications, and solvers
¥ How ARMA(1,1) parameters are estimated in 3dREMLfit
H Optimizing REML log-likelihood function over a discrete grid of (a,b) values, using 2D binary search
H Must solve a GLSQ problem for each (a,b) tested, for each voxel
¥ How statistics are implemented as GLTs
H Testing null hypothesis Gb=0 for arbitrary matrix G
¥ Derivation of ARMA(1,1) formulas
H For completeness, and because we all love equations