The ensemble Kalman filter is an ABC algorithm

The ensemble Kalman filter is the method of choice for many difficult high-dimensional filtering problems in meteorology, oceanography, hydrology and other fields. In this note we show that a common variant of the ensemble Kalman filter is an approximate Bayesian computation (ABC) algorithm. This is of interest for a number of reasons. First, the ensemble Kalman filter is an example of an ABC algorithm that predates the development of ABC algorithms. Second, the ensemble Kalman filter is used for very high-dimensional problems, whereas ABC methods are normally applied only in very low-dimensional problems. Third, recent state of the art extensions of the ensemble Kalman filter can also be understood within the ABC framework.