E. Statistical Inference

In 29  Probability versus Statistics, we discussed how statistics can be regarded as the inverse of probability. Whereas probability quantifies the chances of observing data from a given model, statistics allows us to infer properties of the model from the observed data. So far, we have focused on only one form of statistical inference: estimation. In this unit, we will examine other forms of statistical inference: hypothesis testing and confidence interval. We will also contrast the approach to statistical inference so far, which can be called frequentist, with another approach, called Bayesian.

This unit will require that we use all of the tools that we have developed so far, from asymptotics to multivariate distributions. Therefore, it is a fitting finale to this journey.