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 debunk a common working assumption in the field, saying that in the linear Gaussian regime, the Bayesian posterior can only be recovered with the mean-field limit and not with finite sample sizes or deterministic EKI .