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Demonstrate that the Jeffreys' prior for the mean and variance parameters of normally distributed data $x=\{x_1,x_2,x_3,...,x_n\}$ is given by $p(\theta,\phi)\propto \phi^{-3/2}$.

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closed as off-topic by jbowman, mdewey, Juho Kokkala, Michael Chernick, Silverfish Feb 27 '18 at 19:37

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Self-study questions (including textbook exercises, old exam papers, and homework) that seek to understand the concepts are welcome, but those that demand a solution need to indicate clearly at what step help or advice are needed. For help writing a good self-study question, please visit the meta pages." – jbowman, mdewey, Juho Kokkala, Michael Chernick, Silverfish
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This looks like self study - what have you done to attempt to solve this yourself? $\endgroup$ – probabilityislogic Feb 27 '18 at 13:52
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    $\begingroup$ Is this homework? If so, it should be tagged 'self-study'. I think you should give some more background information, regardless. For example, what is $\phi$ and $\theta$ $\endgroup$ – KenHBS Feb 27 '18 at 13:52
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Hint 1: find the square root of the determinant of the Fisher information matrix, and you have your answer. The determinant of a diagonal matrix is the product of the diagonal entries.

Hint 2: decide whether the variance or the standard deviation is your scale parameter, and stick with that. If you choose the variance, you're taking derivatives with respect to the variance. Some people write the variance as $\sigma^2$, and take derivatives with respect to $\sigma$; this is incorrect.

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