  We introduce a novel online Bayesian method for the identification of a
family of noisy recurrent neural networks (RNNs). We develop Bayesian active
learning technique in order to optimize the interrogating stimuli given past
experiences. In particular, we consider the unknown parameters as stochastic
variables and use the D-optimality principle, also known as `\emph{infomax
method}', to choose optimal stimuli. We apply a greedy technique to maximize
the information gain concerning network parameters at each time step. We also
derive the D-optimal estimation of the additive noise that perturbs the
dynamical system of the RNN. Our analytical results are approximation-free. The
analytic derivation gives rise to attractive quadratic update rules.
