ABSTRACT
We have seen that many simple Bayesian analyses based on noninformative prior distributions give similar results to standard non-Bayesian approaches (for example, the posterior t interval for the normal mean with unknown variance). The extent to which a noninformative prior distribution can be justified as an objective assumption depends on the amount of information available in the data: in the simple cases discussed in Chapters 2 and 3, it was clear that as the sample size n increases, the influence of the prior distribution on posterior inferences decreases. These ideas, sometimes referred to as asymptotic theory, because they refer to properties that hold in the limit as n becomes large, will be reviewed in the present chapter, along with some more explicit discussion of the connections between Bayesian and non-Bayesian methods. The large-sample results are not actually necessary for performing Bayesian data analysis but are often useful as approximations and as tools for understanding.
