  Many applications, such as intermittent data assimilation, lead to a
recursive application of Bayesian inference within a Monte Carlo context.
Popular data assimilation algorithms include sequential Monte Carlo methods and
ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian
inference is implemented. Sequential Monte Carlo methods rely on importance
sampling combined with a resampling step while EnKFs utilize a linear
transformation of Monte Carlo samples based on the classic Kalman filter. While
EnKFs have proven to be quite robust even for small ensemble sizes, they are
not consistent since their derivation relies on a linear regression ansatz. In
this paper, we propose another transform method, which does not rely on any a
prior assumptions on the underlying prior and posterior distributions. The new
method is based on solving an optimal transportation problem for discrete
random variables.
