Survey design for Spectral Energy Distribution fitting: a Fisher Matrix
  approach
  The spectral energy distribution (SED) of a galaxy contains information on
the galaxy's physical properties, and multi-wavelength observations are needed
in order to measure these properties via SED fitting. In planning these
surveys, optimization of the resources is essential. The Fisher Matrix
formalism can be used to quickly determine the best possible experimental setup
to achieve the desired constraints on the SED fitting parameters. However,
because it relies on the assumption of a Gaussian likelihood function, it is in
general less accurate than other slower techniques that reconstruct the
probability distribution function (PDF) from the direct comparison between
models and data. We compare the uncertainties on SED fitting parameters
predicted by the Fisher Matrix to the ones obtained using the more thorough PDF
fitting techniques. We use both simulated spectra and real data, and consider a
large variety of target galaxies differing in redshift, mass, age, star
formation history, dust content, and wavelength coverage. We find that the
uncertainties reported by the two methods agree within a factor of two in the
vast majority (~ 90%) of cases. If the age determination is uncertain, the
top-hat prior in age used in PDF fitting to prevent each galaxy from being
older than the Universe needs to be incorporated in the Fisher Matrix, at least
approximately, before the two methods can be properly compared. We conclude
that the Fisher Matrix is a useful tool for astronomical survey design.
