A Comparative analysis of Bayesian and Frequentist approaches to linear regression

Kolkman, Oskar (2021) A Comparative analysis of Bayesian and Frequentist approaches to linear regression. Bachelor's Thesis, Mathematics.

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Abstract

There are two different methods to estimate the parameters of a linear regression model: the frequentist and the Bayesian approach. This paper aims to present a more comprehensive examination of these two methods. The paper first considers the theoretical foundation of the linear regression model and the frequentist technique. Thereafter the fundamentals of Bayesian statics and the Bayesian approach are discussed. Furthermore two ways to do variable selection for the frequentist approach and the principle of cross-validation will be reviewed. Using the Boston housing data set a simulation study will be performed in which two the following estimators will be compared: ordinary least squares, Lasso, ordinary least squares in combination with backward stepwise model selection using AIC, Gibbs sampling with an uninformative prior and Gibbs sampling with an informative prior. The methods are compared using ten different sample sizes with the mean absolute deviation, the root mean square error and the mean squared error as the measures of fit.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Grzegorczyk, M.A. and Hirsch, C.P.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	20 Jul 2021 13:25
Last Modified:	20 Jul 2021 13:25
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/25314

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