The Bayesian linear regression was named after the English statistician Thomas Bayes, who lived in the first half of the 18th century. The purpose of this bachelors' thesis is to present the basic ideas of Bayesian linear modeling, starting with the theory behind Bayesian statistics, as well as some practical examples of Bayesian linear regression. Regression analysis and its application are described at the beginning. In more detail is discussed the Bayesian statistics and the derivation of the form, which is based on the Bayesian theorem and is the basis on which Bayes' reasoning is based. Also included is the practical application of Bayesian theorem and updating in the case of testing for the presence of a disease state in a patient. Described and on an instructive example of a coin flip is presented the estimation of parameters with the Bayesian approach and its differences and advantages in comparison with the frequency approach of parameter estimation. A normal linear regression model is given. A classical linear regression is presented on it, where the maximum probability method is used to estimate the parameters. As the main part of the thesis, the Bayesian linear regression is described on a normal linear regression model, where we use the Bayesian approach to estimate the parameters. A joint a posteriori distribution of the parameters of the normal model over conjugated families is derived. Finally, Bayes 'update and a posteriori distribution of parameters are also presented in the case of the impact of NBA basketball players' statistics on their salary.
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