Find the prior rather than recalling it

Topic: Conjugate analysis for normal models · more questions on this topic
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Start only with the likelihood kernel (\sigma^2)^{-n/2}\exp\{-S/(2\sigma^2)\}. Test exponential, \chi^2, and Gamma candidates against its support and algebra. Show why a Gamma prior for 1/\sigma^2, rather than for \sigma^2, produces conjugacy.

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