In next-generation cosmology and exoplanet experiments, the data
volumes are large but the signals of greatest importance are tiny.
For examples, think of the baryon acoustic feature in the two-point
correlation function of intergalactic absorption systems or the
discovery of low-mass exoplanets in the astrometry of millions of
parent stars.  In this regime (large data but small signals) utmost
care is required to transfer without loss the relevant information
from the raw data into the parameters of interest. Information
transfer is maximized when inference is performed by modeling the
data, where the "model" generates the mean (expectation) and noise in
the data accurately, but also includes well-informed prior probability
distributions over nuisance parameters. (In general, large numbers of
nuisance parameters are required to perform precise modeling, and
there are technical challenges to marginalizing them out). I will
present some examples of success in these areas---discoveries of
high-redshift quasars, brown-dwarf stars, and exoplanets---and relate
them to Gaia, LSST, and other large projects.