Conjugate Bayesian Modeling of High-Dimensional Count Valued Survey Data Under Informative Sampling Designs

Date: 
03/06/2020 - 4:00pm
Location: 
MDS 220
Speaker(s) / Presenter(s): 
Dr. Scott Holan

We introduce a computationally efficient Bayesian model for predicting high-dimensional dependent count-valued data. In this setting, the Poisson data model with a latent Gaussian process model has become the de facto model. However, this model can be difficult to use in high dimensional settings, where the data may be tabulated over different variables, geographic regions, and times. These computational difficulties are further exacerbated by acknowledging that count-valued data are naturally non-Gaussian. Thus, many of the current approaches, in Bayesian inference, require one to carefully calibrate a Markov chain Monte Carlo (MCMC) technique. We avoid MCMC methods that require tuning by developing a new conjugate multivariate distribution. To incorporate dependence between variables, regions, and time points, a multivariate spatio-temporal mixed effects model (MSTM) is used, resulting in an area-level model. In contrast, unit-level models for survey data offer many advantages over their area-level counterparts, such as potential for more precise estimates and a natural benchmarking property. However, two main challenges occur in this context: accounting for an informative survey design and handling non-Gaussian data types. The pseudo-likelihood approach is one solution to the former, and conjugate multivariate distribution theory offers a solution to the latter. By combining these approaches, we attain a unit-level model for count data that accounts for informative sampling designs and includes fully Bayesian model uncertainty propagation. Importantly, conjugate full conditional distributions hold under the pseudo-likelihood, yielding an extremely computationally efficient approach. Our methods are illustrated using data obtained from the US Census Bureau’s American Community Survey (ACS) and Longitudinal Employer-Household Dynamics (LEHD) program.

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