Parametric Statistical Models

Abstract

Now that we have introduced probability models, we have the tools we need to put our statisticians’ hats on. We want to make a probabilistic model that best describes the world around us. How is it that we can best move from our set of observations to a good model—a model that not only describes our samples, but the process that generated them? In this chapter, we start by making the assumption that the observed data follow a probability model, whose properties are described by a set of parameters. Now that we have this data, the statistical question is: how can we draw information from the samples about the parameters of the distributions that generated them? One basic assumption that aids this process enormously is that of independence.