  A Poisson Binomial distribution over $n$ variables is the distribution of the
sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm
for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we
have sample access is a Poisson Binomial distribution, or far from all Poisson
Binomial distributions. The sample complexity of our algorithm is $O(n^{1/4})$
to which we provide a matching lower bound. We note that our sample complexity
improves quadratically upon that of the naive "learn followed by tolerant-test"
approach, while instance optimal identity testing [VV14] is not applicable
since we are looking to simultaneously test against a whole family of
distributions.
