  In this work we study the problem of inferring a discrete probability
distribution using both expert knowledge and empirical data. This is an
important issue for many applications where the scarcity of data prevents a
purely empirical approach. In this context, it is common to rely first on an
initial domain knowledge a priori before proceeding to an online data
acquisition. We are particularly interested in the intermediate regime where we
do not have enough data to do without the initial expert a priori of the
experts, but enough to correct it if necessary. We present here a novel way to
tackle this issue with a method providing an objective way to choose the weight
to be given to experts compared to data. We show, both empirically and
theoretically, that our proposed estimator is always more efficient than the
best of the two models (expert or data) within a constant.
