Notation in Bayesian hierachical models: what does * indicate I am new to Bayesian Statistics and have a question about the notation *.
What does it indicate in the context of hierarchical models ?
Cheers

I've seen mostly seen $*$ used when you have items $i=1,\ldots,I$ for which you have random effects, say, $\theta_i \sim N(0, \tau^2)$ and you've observed some data. Then you have some estimates $\hat{\theta}_i$ for each of those $\theta_i$. So, when you predict something for these items $i=1,\ldots,I$, you condition on the estimate of the random effect for these items (or in the Bayesian setting, you condition for each MCMC sample $k=1,\ldots,K$ on the estimate $\hat{\theta}_i^{(k)}$).
A different situation arises, when you are trying to predict for a new item, for which you have no data. That often gets index with $*$ and you predict essentially by sampling $\theta_*$ from $N(0, \hat{\tau}^2)$. Or, in the Bayesian seetting, you draw $\hat{\theta}_i^{(k)} \sim N(0, {\hat{\tau}^{(k)}}^2)$.
Why do I keep mentioning the Bayesian setting? Mostly, because that handles the uncertainty about the estimates of the $\theta_i$ and $\tau$ "better" when making new predictions.
