Timeline for Posterior distribution under Cauchy prior?
Current License: CC BY-SA 3.0
10 events
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| Jul 7, 2016 at 20:05 | history | tweeted | twitter.com/StackStats/status/751145121329078272 | ||
| Jul 6, 2016 at 18:29 | comment | added | Chucky | Yes... but the point is to look for the conditional posterior for $\sigma^\eta$. Under an Inverted-Gamma prior, it has a closed form solution. But I want to know if there is a closed form solution also under a half Cauchy prior, or if I will have no other option than to use an MH step in the simulation | |
| Jul 6, 2016 at 16:23 | comment | added | Xi'an | Given the hierarchical nature of your model, the first equation is irrelevant for the simulation of $\sigma^\eta$. And once the $X_t$'s have been simulated, you end up with an iid sample from a Normal(0,\sigma^\eta)$, that is, the simplest possible case. | |
| Jul 5, 2016 at 19:25 | comment | added | Chucky | Thanks guys! I edited the question, just in case it is more clear | |
| Jul 5, 2016 at 19:11 | history | edited | Chucky | CC BY-SA 3.0 |
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| Jul 5, 2016 at 18:30 | comment | added | Björn | I think those papers do tell you how to construct the conditional conjugate by parameter expansion (introducing a third parameter - I think e.g. "Prior distributions for variance parameters in hierarchical models(Comment on Article by Browne and Draper)" by Gelman has the details, pages 519-520). | |
| Jul 5, 2016 at 17:16 | comment | added | Sycorax♦ | I think you mean half-Cauchy, since a Cauchy distribution has support over the reals and a valid variance must be nonnegative. | |
| Jul 5, 2016 at 17:13 | history | edited | Sycorax♦ | CC BY-SA 3.0 |
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| Jul 5, 2016 at 17:04 | comment | added | whuber♦ | Did you really mean to write "conjugate"? | |
| Jul 5, 2016 at 16:36 | history | asked | Chucky | CC BY-SA 3.0 |