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Chapter 3: Bayesian Estimation of Regression Models
Bayesian statistics provide an alternative to the maximum likelihood principle for the estimation of regression models. While maximum likelihood assumes a true value for a parameter and describes its estimator, including the standard error, the Bayesian statistics framework assumes a certain distribution as an inherent part of the parameter. This seemingly trivial difference has some important consequences in parameter estimation of statistical models, including regression models. To make this point clear, we explicate the difference between Bayesian statistics and maximum likelihood in what follows.
In the maximum likelihood framework, a single data set is interpreted as one realization of potential data sets. This is very simple to understand if one ...