Introduction to Bayesian Thinking

In this chapter, the basic elements of the Bayesian inferential approach are introduced through the basic problem of learning about a population proportion. Before taking data, one has beliefs about the value of the proportion and one models his or her beliefs in terms of a prior distribution. We will illustrate the use of different functional forms for this prior. After data have been observed, one updates one’s beliefs about the proportion by the computation of the posterior distribution. One summarizes this probability distribution to perform inferences. Also one may be interested in predicting the likely outcomes of a new sample taken from the population.