TY  - JOUR
A1  - Reich, Sebastian
T1  - A nonparametric ensemble transform method for bayesian inference
JF  - SIAM journal on scientific computing
N2  - 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 priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.
KW  - Bayesian inference
KW  - Monte Carlo method
KW  - sequential data assimilation
KW  - linear programming
KW  - resampling
Y1  - 2013
U6  - https://doi.org/10.1137/130907367
SN  - 1064-8275
VL  - 35
IS  - 4
SP  - A2013
EP  - A2024
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -