rigliztetbf
2022-06-26
Raven Higgins
Beginner2022-06-27Added 17 answers
If anyone runs into the similar section in Gelman's book, I'm going to give my own solution that I came up with below (pages 110-111).
By this, the author only implies that
Answer (2):
When the author refers to a "appropriate Jacobian," he is referring to the Jacobian matrix's determinant in the formula for density functions with changed variables:
Answer (3):
Simply said, the author uses the change of variables formula twice. The fact that
If we denote and ), then:
From the formula for variable change, we obtain:
and there it is, i.e. the prior in original scale.
By using the exact same modification of variables for the alternate scale:
where this time and We obtain: for the Jacobian determinant.
so we get:
or
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5, 17
2, 20
4, 18
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A)
B)
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D)
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