  With the ubiquitous availability of unstructured data, growing attention is
paid as how to adjust for selection bias in such non-probability samples. The
majority of the robust estimators proposed by prior literature are either fully
or partially design-based, which may lead to inefficient estimates if outlying
(pseudo-)weights are present. In addition, correctly reflecting the uncertainty
of the adjusted estimator remains a challenge when the available reference
survey is complex in the sample design. This article proposes a fully
model-based method for inference using non-probability samples where the goal
is to predict the outcome variable for the entire population units. We employ a
Bayesian bootstrap method with Rubin's combing rules to derive the adjusted
point and interval estimates. Using Gaussian process regression, our method
allows for kernel matching between the non-probability sample units and
population units based on the estimated selection propensities when the outcome
model is misspecified. The repeated sampling properties of our method are
evaluated through two Monte Carlo simulation studies. Finally, we examine it on
a real-world non-probability sample with the aim to estimate crash-attributed
injury rates in different body regions in the United States.
