  In this paper, we apply a new statistical analysis technique, Mean Field
approach to Bayesian Independent Component Analysis (MF-ICA), on galaxy
spectral analysis. This algorithm can compress the stellar spectral library
into a few Independent Components (ICs), and galaxy spectrum can be
reconstructed by these ICs. Comparing to other algorithms which decompose a
galaxy spectrum into a combination of several simple stellar populations,
MF-ICA approach offers a large improvement in the efficiency. To check the
reliability of this spectral analysis method, three different methods are used:
(1) parameter-recover for simulated galaxies, (2) comparison with parameters
estimated by other methods, and (3) consistency test of parameters from the
Sloan Digital Sky Survey galaxies. We find that our MF-ICA method not only can
fit the observed galaxy spectra efficiently, but also can recover the physical
parameters of galaxies accurately. We also apply our spectral analysis method
to the DEEP2 spectroscopic data, and find it can provide excellent fitting for
those low signal-to-noise spectra.
