  We study two possible explanations for short baseline neutrino oscillation
anomalies, such as the LSND and MiniBooNE anti-neutrino data, and for the
reactor anomaly. The first scenario is the mini-seesaw mechanism with two
eV-scale sterile neutrinos. We present both analytic formulas and numerical
results showing that this scenario could account for the short baseline and
reactor anomalies and is consistent with the observed masses and mixings of the
three active neutrinos. We also show that this scenario could arise naturally
from an effective theory containing a TeV-scale VEV, which could be related to
other TeV-scale physics. The minimal version of the mini-seesaw relates the
active-sterile mixings to five real parameters and favors an inverted
hierarchy. It has the interesting property that the effective Majorana mass for
neutrinoless double beta decay vanishes, while the effective masses relevant to
tritium beta decay and to cosmology are respectively around 0.2 and 2.4 eV. The
second scenario contains only one eV-scale sterile neutrino but with an
effective non-unitary mixing matrix between the light sterile and active
neutrinos. We find that though this may explain the anomalies, if the
non-unitarity originates from a heavy sterile neutrino with a large
(fine-tuned) mixing angle, this scenario is highly constrained by cosmological
and laboratory observations.
