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We introduce Bayesian hierarchical models for predicting high-dimensionaltabular survey data which can be distributed from one or multiple classes ofdistributions (e.g., Gaussian, Poisson, Binomial, etc.). We adopt a Bayesianimplementation of a Hierarchical Generalized Transformation (HGT) model to dealwith the non-conjugacy of non-Gaussian data models when estimated using aLatent Gaussian Process (LGP) model. Survey data are usually prone to a highdegree of sampling error, and we use covariates that are prone to measurementerror as well as those free of any such error. A classical measurement errorcomponent is defined to deal with the sampling error in the covariates. Theproposed models can be high-dimensional and we employ the notion of basisfunction expansions to provide an effective approach to dimension reduction.The HGT component lends flexibility to our model to incorporate multi-typeresponse datasets under a unified latent process model framework. Todemonstrate the applicability of our methodology, we provide the results fromsimulation studies and data applications arising from a dataset consisting ofthe U.S. Census Bureau's American Community Survey (ACS) 5-year periodestimates of the total population count under the poverty threshold and the ACS5-year period estimates of median housing costs at the county level acrossmultiple states in the USA.

Bayesian Hierarchical Models For Multi-type Survey Data Using Spatially Correlated Covariates Measured With Error