Bayesian Inference by Hanns Ludwig Harney

Author:Hanns Ludwig Harney
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(8.31)

to the first order in .

In the following section, the linear representation of the symmetry of dilation is derived.

8.5 The Linear Representation of Dilation

We can use the linear operator of translation to construct the linear operator of dilation. Consider again the model with the structure of (3.​9),

(8.32)

To begin we assume the event variable x to be positive; this assumption can be dropped later on.

We want to bring the linear transformation of the probability amplitude (8.17) of this model into a form similar to Eq. (8.30). We show in Chap. 9 that this requires the measure of the parameter to be uniform, whence must be transformed according to

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