  Big Data often presents as massive non-probability samples. Not only is the
selection mechanism often unknown, but larger data volume amplifies the
relative contribution of selection bias to total error. Existing bias
adjustment approaches assume that the conditional mean structures have been
correctly specified for the selection indicator or key substantive measures. In
the presence of a reference probability sample, these methods rely on a
pseudo-likelihood method to account for the sampling weights of the reference
sample, which is parametric in nature. Under a Bayesian framework, handling the
sampling weights is an even bigger hurdle. To further protect against model
misspecification, we expand the idea of double robustness such that more
flexible non-parametric methods as well as Bayesian models can be used for
prediction. In particular, we employ Bayesian additive regression trees, which
not only capture non-linear associations automatically but permit direct
quantification of the uncertainty of point estimates through its posterior
predictive draws. We apply our method to sensor-based naturalistic driving data
from the second Strategic Highway Research Program using the 2017 National
Household Travel Survey as a benchmark.
