Notes on Statistical Decision Theory and Bayesian Analysis Bayesian Statistics

• Up to this point, we considered parameters to be fixed (but unknown) numbers. While discussing inference in this framework (estimation and hypothesis testing), we evaluated the properties of estimators and tests when applied repeatedly to the same problem, i.e. with the same true parameter value but different draws. For instance, an unbiased estimator is one with a sampling distribution whose mean is equal to the true parameter value, or a level α test rejects the true null hypothesis on average over repeated samples with probability α. This form of evaluation hence averages the performance over different draws from the same model (with fixed parameter). This is the traditional approach, and is thus often called ’classical’ statistics, or ’frequentist’.