Dropping Observations without Affecting Posterior and Predictive Distributions.

摘要

Suppose in a distribution problem, the sample information W is split into two pieces W sub 1 and W sub 2 prime and the parameters involved are split into two sets phi containing the parameters of interest, and theta containing nuisance parameters. It is shown that, under certain conditions, the posterior distribution of phi does not depend on the data W sub 2 prime which can thus be ignored. This also has consequences for the predictive distribution of future (or missing) observations. In fact, under similar conditions, the predictive distributions using W or just W sub 1 are identical.