  We introduce Bayesian hierarchical models for predicting high-dimensional
tabular survey data which can be distributed from one or multiple classes of
distributions (e.g., Gaussian, Poisson, Binomial, etc.). We adopt a Bayesian
implementation of a Hierarchical Generalized Transformation (HGT) model to deal
with the non-conjugacy of non-Gaussian data models when estimated using a
Latent Gaussian Process (LGP) model. Survey data are usually prone to a high
degree of sampling error, and we use covariates that are prone to measurement
error as well as those free of any such error. A classical measurement error
component is defined to deal with the sampling error in the covariates. The
proposed models can be high-dimensional and we employ the notion of basis
function expansions to provide an effective approach to dimension reduction.
The HGT component lends flexibility to our model to incorporate multi-type
response datasets under a unified latent process model framework. To
demonstrate the applicability of our methodology, we provide the results from
simulation studies and data applications arising from a dataset consisting of
the U.S. Census Bureau's American Community Survey (ACS) 5-year period
estimates of the total population count under the poverty threshold and the ACS
5-year period estimates of median housing costs at the county level across
multiple states in the USA.
