  We present a scalable and robust Bayesian inference method for linear state
space models. The method is applied to demand forecasting in the context of a
large e-commerce platform, paying special attention to intermittent and bursty
target statistics. Inference is approximated by the Newton-Raphson algorithm,
reduced to linear-time Kalman smoothing, which allows us to operate on several
orders of magnitude larger problems than previous related work. In a study on
large real-world sales datasets, our method outperforms competing approaches on
fast and medium moving items.
