  We combine Bayesian prediction and weighted inference as a unified approach
to survey inference. The general principles of Bayesian analysis imply that
models for survey outcomes should be conditional on all variables that affect
the probability of inclusion. We incorporate the weighting variables under the
framework of multilevel regression and poststratification, as a byproduct
generating model-based weights after smoothing. We investigate deep
interactions and introduce structured prior distributions for smoothing and
stability of estimates. The computation is done via Stan and implemented in the
open source R package "rstanarm" ready for public use. Simulation studies
illustrate that model-based prediction and weighting inference outperform
classical weighting. We apply the proposal to the New York Longitudinal Study
of Wellbeing. The new approach generates robust weights and increases
efficiency for finite population inference, especially for subsets of the
population.
