Timeline for Interpretation of posterior distribution for Gelman's Rat Example
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2018 at 15:06 | comment | added | Robin Ryder | You would have $\theta_{72}|\alpha,\beta\sim Beta(\alpha, \beta)$. To get a realization of $\theta_{72}$, sample $\alpha$ and $\beta$ from the posterior, and then $\theta_{72}$ from this conditional distribution. | |
| Nov 26, 2018 at 15:03 | vote | accept | Demetri Pananos | ||
| Nov 26, 2018 at 14:31 | comment | added | Robin Ryder | There is no closed form for the marginal posterior of $\theta_j$. Conditionally on the values of $\alpha$ and $\beta$, the $\theta_j$ come from a Beta distribution. However, $\alpha$ and $\beta$ are not known exactly: we have a distribution for them as well. To get a sample from the distribution of $\theta_j$, you need to draw samples from the marginal posterior of $(\alpha, \beta)$, and then for each of those samples draw from the conditional posterior $\theta_j\sim Beta(\alpha+y_j,\beta+n_j-y_j)$. | |
| Nov 26, 2018 at 12:53 | comment | added | Demetri Pananos | So am I right to interpret the model as follows: that each $\theta_j$ come from a beta distribution with parameters alpha and beta, and that the alpha and beta are obtained from the marginal posterior (i.e. the mean of 5.8)? | |
| Nov 26, 2018 at 9:28 | history | answered | Robin Ryder | CC BY-SA 4.0 |