  We study decision problems under uncertainty, where the decision-maker has
access to $K$ data sources that carry {\em biased} information about the
underlying risk factors. The biases are measured by the mismatch between the
risk factor distribution and the $K$ data-generating distributions with respect
to an optimal transport (OT) distance. In this situation the decision-maker can
exploit the information contained in the biased samples by solving a
distributionally robust optimization (DRO) problem, where the ambiguity set is
defined as the intersection of $K$ OT neighborhoods, each of which is centered
at the empirical distribution on the samples generated by a biased data source.
We show that if the decision-maker has a prior belief about the biases, then
the out-of-sample performance of the DRO solution can improve with $K$ --
irrespective of the magnitude of the biases. We also show that, under standard
convexity assumptions, the proposed DRO problem is computationally tractable if
either $K$ or the dimension of the risk factors is kept constant.
