Author

Shucen A. Liu

Date of Graduation

Fall 2012

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Songfeng Zheng

Keywords

least square, maximum likelihood estimation, bayesian estimation, gibbs sampler, linear regression model

Subject Categories

Mathematics

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.

Copyright

© Shucen A. Liu

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