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I am currently doing an undergraduate mathematical statistics course. One questions in Bayesian methods that i can’t seem to grasp is knowing when to use an improper uniform prior? After learning conjugate priors, my instincts are to directly go on to use conjugate priors whenever possible. However some times in the solution manual, it uses an improper uniform prior. Is there a trick to knowing when to use an improper uniform prior than a conjugate prior? Thank you.

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  • $\begingroup$ Sometimes an improper uniform prior can be seen a a limiting version of a conjugate distribution. For example for a normal distribution with unknown mean but known variance or precision, the conjugate prior can be a normal distribution and you can start with infinite variance / zero precision $\endgroup$ – Henry 2 days ago

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