  We provide bivariate asymptotics for the poly-Bernoulli numbers, a
combinatorial array that enumerates lonesum matrices, using the methods of
Analytic Combinatorics in Several Variables (ACSV). For the diagonal asymptotic
(i.e., for the special case of square lonesum matrices) we present an
alternative proof based on Parseval's identity. In addition, we provide an
application in Algebraic Statistics on the asymptotic ML-degree of the
bivariate multinomial missing data problem, and we strengthen an existing
result on asymptotic enumeration of permutations having a specified excedance
set.
