  Despite the rapid progression in our understanding of neutrinos over the last
half century, much is left unknown about their properties. This leaves
neutrinos as the most promising portal for Beyond Standard Model (BSM) physics,
and neutrinos have already provided fruitful surprises.
  A number of neutrino experiments in the last three decades have observed
anomalous oscillation signals consistent with a mass-squared splitting of
$\Delta m^2 \sim 1\ \textrm{eV}^2$, motivating the existence and search for
sterile neutrinos. On the other hand, other experiments have failed to see such
a signal.
  In this thesis, we present two analyses. The first is an update to the
sterile neutrino global fits with the inclusion of recent experimental data. We
find that the 3+1 model provides a better fit to the global data set compared
to the null, with an improvement of $\Delta \chi^2 = 51$ with the addition of
only 3 degrees of freedom, corresponding to $6.6\sigma$. While a substantial
improvement, we also find a irreconcilable tension between the data sets of
$5.1\sigma$, calculated using the parameter goodness-of-fit test. This
motivates the exploration of expanded models: a 3+2 model, and a 3+1+Decay
model. In the 3+2 model, we find negligible improvement to the fit, and an even
worse tension of $5.5\sigma$. In the more exotic 3+1+Decay model, we find the
tension reduced to $3.6\sigma$. While a substantial improvement compared to the
3+1 model with the introduction of only one additional parameter, the tension
is still too large to assuage concerns.
  The second analysis is the results of an expanded IceCube sterile neutrino
search. A previous sterile neutrino search found no evidence for sterile
neutrinos, finding a p-value of 8%. Of the three sterile mixing angles,
$\theta_{14}, \theta_{24}$, and $\theta_{34}$, only $\theta_{24}$ was fitted
for, as $\theta_{14}$ was negligible and $\theta_{34} = 0$ was considered a
conservative assumption. We present results of an analysis where we include
$\theta_{34}$ to the fitted model. Both a frequentist and Bayesian analysis
were conducted, with fits done in terms of the mass-squared splitting $\Delta
m_{41}^2$ and the mixing matrix parameters $|U_{\mu4}|^2$ and $|U_{\tau4}|^2$.
The frequentist analysis finds a best fit at $\Delta m_{41}^2 = 5.0\
\textrm{eV}^2$, $|U_{\mu4}|^2 = 0.04$, and $|U_{\tau4}|^2 = 0.006$, with a
p-value of 5.2% assuming Wilks' Theorem with 3 degrees of freedom.
Pseudoexperiments are indicating a smaller p-value 2.7%. The Bayesian analysis
finds a similar best fit point at $\Delta m_{41}^2 = 5.0\ \textrm{eV}^2$,
$|U_{\mu4}|^2 = 0.02$, and $|U_{\tau4}|^2 = 0.006$, with a Bayes factor
indicating a ``Very Strong'' preference for this sterile hypothesis over the
null hypothesis.
