Bayesian Hierarchical Models That Incorporate New Sources of Dependence for Boundary Detection and Spatial Prediction

• Other Authors: Qu, Kai (author)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Statistics
• Online Access: http://purl.flvc.org/fsu/fd/2019_Fall_Qu_fsu_0071E_15498

Spatial boundary analysis has attained considerable attention in several disciplines including engineering, spatial statistics, and computer science. The inferential question of interest is to identify rapid surface changes of an unobserved latent process. We extend Curvilinear Wombling, the current state-of-art method for point referenced data that is curve measure based and limited to a single spatial scale, to multiscale settings. Specifically, we propose a multiscale representation of the directional derivative of Karhunen-Lo'eve (DDKL) expansion to perform multiscale direction-based boundary detection. By aggregating curvilinear wombling measure, we extend curvilinear boundary detection from curve to zone. Furthermore, we propose a direction-based multiscale curvilinear boundary error criterion to quantify curvilinear boundary fallacy (CBF), which is an analogue to the ecological fallacy in the spatial change of support literature. We refer to this metric as the criterion for boundary aggregation error (BAGE). Several theoretical results are derived to motivate BAGE. Particularly, we show that no boundary aggregation error exists when directional derivatives of eigenfunctions of a Karhunen-Lo'eve expansion are constant across spatial scales. We illustrate the use of our model through a simulated example and an application of Mediterranean wind measurements. The American Community Survey (ACS) is an ongoing survey administered by the U.S. Census Bureau, which publishes estimates of important demographic statistics over pre-specified administrative areas periodically. Spatially referenced binomial count data are widely present in ACS. Since the sample size of a binomial count is often a realization of a random process, the probability of an outcome and the probability of a trial number are possibly correlated. We consider a joint model for both binomial outcome and the trial number. Latent Gaussian process (LGP) models are widely used to analyze for non-Gaussian ACS count data. However, there are computational problems; for example, LGPs may involve subjective tuning of parameters using Metroplis-Hastings. To improve computational performance of Gibbs sampling, we include the latent multivariate logit-beta distribution (MLB) in our joint model for binomial and negative binomial count data. The closed form full-conditional distributions are straightforward to simulate from without subjective tuning steps within a Gibbs sampler. We illustrate the proposed model through simulations and an application of ACS poverty estimates at the county level. === A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === 2019 === October 24, 2019. === Includes bibliographical references. === Jonathan R. Bradley, Professor Co-Directing Dissertation; Xufeng Niu, Professor Co-Directing Dissertation; Kevin Speer, University Representative; Fred Huffer, Committee Member.