Before revision:  In particular, we debunk a common working assumption in the field, saying that in the linear Gaussian regime, the empirical measure at time t=1 is a surrogate for the posterior , i.e., the correct Bayesian answer to the inverse problem .
After revision:  In particular, we analyze dynamics of deterministic EKI, averaged quantities of stochastic EKI, and mean-field EKI. We show that in the linear Gaussian regime, the empirical measure at time t=1 is a surrogate for the posterior , i.e., the correct Bayesian answer to the inverse problem .