  We introduce a hierarchical Bayesian approach to tackle the challenging
problem of size recommendation in e-commerce fashion. Our approach jointly
models a size purchased by a customer, and its possible return event: 1. no
return, 2. returned too small 3. returned too big. Those events are drawn
following a multinomial distribution parameterized on the joint probability of
each event, built following a hierarchy combining priors. Such a model allows
us to incorporate extended domain expertise and article characteristics as
prior knowledge, which in turn makes it possible for the underlying parameters
to emerge thanks to sufficient data. Experiments are presented on real
(anonymized) data from millions of customers along with a detailed discussion
on the efficiency of such an approach within a large scale production system.
