Bayesian meta-analysis with selection models (publication bias)

Here are the Stan and R codes for performing Bayesian meta-analysis with selection models to take into account publication bias (selections).

The assumption applied in the selection models (implemented here) is that the probability one experiment was published depends on its p-value. More specifically:

1. The p-value range (i.e., from 0 to 1) could be divided into several intervals. And within the same interval, the probablities that experiments were published were the same;
2. The probability was higher for the interval with smaller p-values.
3. Experiments in which the p-value was smaller than 0.05 were all published (i.e., with the probability of 100%);

Parts of the weighted probability density distribution is from library(publipha).