Bayesian Statistics: An Introduction, 4th Edition

8.2 The hierarchical normal model

8.2.1 The model

Suppose that

is a vector of fixed, unknown parameters and that

is a vector of independent observations such that

Of course, the Xi could each be means of a number of observations.

For the moment, we shall suppose that is known, so, after a suitable normalization, we can suppose that .

It is useful to establish some notation for use later on, We shall consider a fixed origin

and we will write

and

for a vector of r elements all equal to unity.

We suppose that on the basis of our knowledge of the Xi we form estimates of the and write

In general, ...