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X-WR-CALNAME:Mathematical Sciences Department PhD Dissertation Defense - Ashley Lockwood, "Bayesian Predictive Inference for a Study Variable Without Specifying a Link to the Covariates" SH203
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URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences-department-phd-dissertation-defense-ashley-lockwood-bayesian-predictive
SUMMARY: Mathematical Sciences Department PhD Dissertation Defense - Ashley Lockwood, "Bayesian Predictive Inference for a Study Variable Without Specifying a Link to the Covariates" SH203
DESCRIPTION:
Mathematical Sciences Department
PhD Dissertation Defense
Ashley Lockwood, Mathematical Sciences PhD Candidate
Wednesday, April 19, 2023
10:00 am - 12:00 pm
Stratton Hall 203
and via Zoom: 930 4205 6158
https://wpi.zoom.us/j/93042056158
Title: Bayesian Predictive Inference for a Study Variable Without Specifying a Link to the Covariates
Abstract: We perform Bayesian predictive inference of a finite population mean for a study (response) variable without specifying a link between the study variable and covariates, consequently overcoming some limitations of traditional regression analysis. For real applications, we take care of three effects (spatial, heterogeneity, and clustering) simultaneously. We have explored several multinomial-Dirichlet models with stick-breaking representation on the mean vector to address a polychotomous regression problem. We also present a continuous regression problem addressed by including a spatial component in our Bayesian hierarchical model. Finally, we demonstrate a solution to the binary predictive inference problem while also incorporating a clustering stick-breaking prior. We illustrate all the models using an application with BMI data. First, to avoid defining the relationship between the study variable and covariates, we use a hierarchical Bayesian multinomial-Dirichlet model with stick-breaking representation on the mean vector to make inference about the characteristics of a finite population. Several versions of multinomial-Dirichlet model are explored: an unordered and ungrouped model, an ordered and grouped model, a pooled area model, and a model with survey weights included. The ordered and grouped model is introduced to reduce the number of parameters drawn in the Gibbs sampler. Lastly, the pooled area model is used to introduce small area estimation techniques. Second, while we avoid specifying the parametric relationship between the study variable and covariates, we illustrate the advantage of including a spatial component to better account for the covariates in our models to make Bayesian predictive inference. The two spatial models used are the conditional autoregressive (CAR) and simple conditional autoregressive models. We also show how to incorporate survey weights into the spatial models when dealing with probability survey data. We treat each unique covariate combination as an individual stratum, then we use small area estimation techniques to make inference. Our goal is to have neighboring areas yield similar predictions, and to increase the difference between areas that are not neighbors. Third, in order to gain robustness, we combine spatial, heterogeneity, and clustering components. After finding success with the CAR model, we use this spatial model joined with a clustering stick-breaking prior to gain more information from the covariates. The main advantage of including a stickbreaking component in our model is that the number of clusters of the strata is determined by the algorithm and is subject to change at every iteration of the blocked Gibbs sampler. The results show that the spatial stick-breaking model outperforms the Fay-Herriot model in both accuracy and precision. We address concerns with traditional regression analysis by providing multiple Bayesian hierarchical models that allow for inference to be made about a study variable including covariates and without the need for estimating regression coefficients. We have successful results that pave the way for further extensions of alternate regression models. Our models expand the scope of applications we can explore with minimal assumptions, when compared to traditional regression models.
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