ABSTRACT
Proportions are like probabilities. In the subjective view of probabilities, one needs to express one’s opinion about the likelihood of a one-time event. The subjective view is one's personal opinion about the location of the unknown proportion. It does require one to express his or her opinion about the value of the proportion, and he or she could be skeptical or unknown about the opinion. This chapter discusses how to express prior opinion that matches with one’s belief, how to extract information from the likelihood, and how to update our opinion to its posterior. It introduces inference when a discrete prior distribution is assigned to the proportion, as well as the beta class of continuous prior distributions. The chapter describes the inference process with a beta prior in detail. It also discusses general Bayesian inference methods for learning about the proportion, namely Bayesian hypothesis testing, Bayesian credible intervals and Bayesian prediction.
