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Bayesian Methods in Semiparametric Regression
Abstract
In a regression setup, one of the most encountered problem is the presence of error in the predictor(s) - also known as measurement error models. A popular way of dealing with measurement error models is a semiparametric approach. However, there still exists a myriad of real-life measurement error problems for which there does not exist a standard efficient solution. The purpose of this research was to delve into some of the existing measurement error problems and develop efficient solutions for them.
This dissertation focuses on three different problems arising in the fields of Oncology and Nutrition where standard approaches to measurement error models fail. For each of these problems, we proposed a novel solution and outlined their implementation using Bayesian estimation methods along with developing the corresponding computational tools required to implement them.
In the first problem we focused on understanding how physical activities influence fatigue levels in breast cancer survivors. The physical activities are measured with error. We proposed a novel solution combining B-splines and the efficient JAGS sampler in R. Our custom R functions using Bayesian methods are available publicly for use. The second problem focuses on computing the percentage of never consumers from a 24-hour dietary recall survey. There are two sources of zero when someone is reporting consumption amounts corresponding to episodic consumption and no consumption ever. With a small number of repeat measurements from individuals, it is not possible to determine those who are episodic zeros and those who are hard zeros. We developed a new measurement error model for this problem and used Bayesian methods to fit it. For the third problem, we focused on another problem in Nutrition which also used data from dietary surveys however for this problem one or some of the consumption amounts were missing. Our goal was to estimate the overall dietary pattern and distribution of usual intake. We proposed a new measurement error model and estimated it using Bayesian methods. Thus, we developed three novel approaches for measurement error models that can be used beyond the problems discussed in this dissertation.
Subject
Semiparametric RegressionBayesian Methods
Measurement Error Models
Hard Zeros
Latent Variables
Citation
Roy Chowdhury, Ananya (2023). Bayesian Methods in Semiparametric Regression. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /198924.