Date of Graduation
Fall 2012
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Songfeng Zheng
Abstract
In recent years, with widely accesses to powerful computers and development of new computing methods, Bayesian method has been applied to many fields including stock forecasting, machine learning, and genome data analysis. In this thesis, we will give an introduction to estimation methods for linear regression models including least square method, maximum likelihood method, and Bayesian method. We then describe Bayesian estimation for linear regression model in detail, and the prior and posterior distributions for different parameters will be derived. This method provides a posterior distribution of the parameters in the linear regression model, so that the uncertainties are integrated. Extensive experiments are conducted on simulated data and real-world data, and the results are compared to those of least square regression. Then we reached a conclusion that Bayesian approach has a better performance when the sample size is large.
Keywords
least square, maximum likelihood estimation, bayesian estimation, gibbs sampler, linear regression model
Subject Categories
Mathematics
Copyright
© Shucen A. Liu
Recommended Citation
Liu, Shucen A., "Bayesian Inference in Linear Regression Models" (2012). MSU Graduate Theses. 1645.
https://bearworks.missouristate.edu/theses/1645
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