  A central theme in the field of survey statistics is estimating
population-level quantities through data coming from potentially
non-representative samples of the population. Multilevel Regression and
Poststratification (MRP), a model-based approach, is gaining traction against
the traditional weighted approach for survey estimates. MRP estimates are
susceptible to bias if there is an underlying structure that the methodology
does not capture. This work aims to provide a new framework for specifying
structured prior distributions that lead to bias reduction in MRP estimates. We
use simulation studies to explore the benefit of these prior distributions and
demonstrate their efficacy on non-representative US survey data. We show that
structured prior distributions offer absolute bias reduction and variance
reduction for posterior MRP estimates in a large variety of data regimes.
