THE NECESSITY OF specifying a prior distribution in Bayesian inference has been regarded by some as an advantage of the approach and by others a disadvantage. On the one hand, the prior distribution allows the researcher to include in a systematic way any information he or she has about the parameters being studied. On the other hand, the researcher's prior information may be very limited or difficult to quantify in the form of a probability distribution, and, as we have seen in Chapter 3, the prior distribution plays a large role in determining the posterior distribution for small samples.

This chapter puts forth, in general terms, some ideas on how to specify prior distributions. The topic is revisited in connection with specific models in Part III. The normal linear regression model, described next, is the primary example for the topics in this chapter.

Normal Linear Regression Model

The normal linear regression model is the workhorse of econometric, and more generally, statistical modeling. We consider it here because of its wide applicability and because it is a relatively easy model with which to illustrate the specification of hyperparameters.