  The declining response rates in probability surveys along with the widespread
availability of unstructured data has led to growing research into
non-probability samples. Existing robust approaches are not well-developed for
non-Gaussian outcomes and may perform poorly in presence of influential
pseudo-weights. Furthermore, their variance estimator lacks a unified framework
and rely often on asymptotic theory. To address these gaps, we propose an
alternative Bayesian approach using a partially linear Gaussian process
regression that utilizes a prediction model with a flexible function of the
pseudo-inclusion probabilities to impute the outcome variable for the reference
survey. By efficiency, we mean not only computational scalability but also
superiority with respect to variance. We also show that Gaussian process
regression behaves as a kernel matching technique based on the estimated
propensity scores, which yields double robustness and lowers sensitivity to
influential pseudo-weights. Using the simulated posterior predictive
distribution, one can directly quantify the uncertainty of the proposed
estimator and derive associated $95\%$ credible intervals. We assess the
repeated sampling properties of our method in two simulation studies. The
application of this study deals with modeling count data with varying exposures
under a non-probability sample setting.
