  In analyzing big data for finite population inference, it is critical to
adjust for the selection bias in the big data. In this paper, we propose two
methods of reducing the selection bias associated with the big data sample. The
first method uses a version of inverse sampling by incorporating auxiliary
information from external sources, and the second one borrows the idea of data
integration by combining the big data sample with an independent probability
sample. Two simulation studies show that the proposed methods are unbiased and
have better coverage rates than their alternatives. In addition, the proposed
methods are easy to implement in practice.
