Conversation
| $$ | ||
| \begin{align} | ||
| y_i \sim \text{gamma}(s, \alpha/exp(\eta)) \\ | ||
| \eta_i = \alpha + \beta \cdot x_i | ||
| \end{align} | ||
| $$ |
There was a problem hiding this comment.
The Gamma distribution can be a tricky one given the different parameterizations.
In PyMC/Bambi/PreliZ we have (alpha, beta) and (mu, sigma) see here for details https://preliz.readthedocs.io/en/latest/examples/gallery/gamma.html
Usually, we use the mu, sigma parametrization like this
\begin{align}
y_i \sim \text{gamma}(\text{mu}=\mu_i, \text{sigma}=\frac{\mu_i}{\alpha^{0.5}}) \
\mu_i = \exp(\eta_i)\
\eta_i = \beta_0 + \beta_1 \cdot x_i
\end{align}
In brms, I think we have (mu, alpha) and Stan use (alpha, beta) [the same as the PyMC's default]
There was a problem hiding this comment.
Good point, there are clear typos here too. However the issue of different parameterizations is something we will run into in various places, also when recommending priors (e.g. exponential prior). I will open an issue about handling different parametrisations in general
WIP