8.2 The hierarchical normal model

8.2.1 The model

Suppose that

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is a vector of fixed, unknown parameters and that

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is a vector of independent observations such that

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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

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and we will write

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and

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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, ...

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