Max Tegmark's cosmology library: karhunen
Figure 1: The derivatives of the CDM power spectrum
with respect to various parameters.
You can get the 450K uncompressed
postscript file by clicking
if you are interested in
other research of mine.
Karhunen-Loeve eigenvalue problems in cosmology:
how should we tackle large data sets?
& Alan Heavens
Since cosmology is no longer "the data-starved science",
the problem of how to best analyze large data sets has
recently received considerable attention, and Karhunen-Loeve
eigenvalue methods have been applied to both galaxy
redshift surveys and Cosmic Microwave Background (CMB) maps.
We present a comprehensive discussion of methods for
estimating cosmological parameters from large data sets, which
includes the previously published techniques as special cases.
We show that both the problem of estimating several parameters jointly
and the problem of not knowing the parameters a priori can be readily
solved by adding an extra singular value decomposition step.
It has recently been argued that the information content in a sky map
from a next generation CMB satellite is sufficient to measure key
cosmological parameters (h, Omega, Lambda, etc) to an accuracy of a
few percent or better - in principle. In practice, the data set is
so large that both a brute force likelihood analysis and a direct
expansion in signal-to-noise eigenmodes will be computationally
unfeasible. Fortunately, we find that a Karhunen-Loeve approach can
nonetheless measure the parameters with almost maximal accuracy,
if preceded by a certain form of quadratic "pre-compression".
We also discuss practical issues regarding parameter estimation from
present and future galaxy redshift surveys, and illustrate this with
a generalized eigenmode analysis of the IRAS 1.2 Jy survey optimized
for measuring beta=Omega^0.6/b using redshift space distortions.
ApJ, 480, 22-35 (1997)
This site also contains the latest versions of some papers that are referenced in
Ted Bunn's PhD thesis,
Tegmark & Bunn 1995,
Tegmark & Efstathiou 1996,
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This page was last modified July 1, 1998.