Selection model for publication bias ($f_{\mathrm{obs}}(y)=f(y)\pi (y)/\int f(v)\pi (v)dv$)

A selection model combines a distribution for all study results with a probability $\pi (y)$ that a result becomes available. The observed distribution is reweighted by this probability and renormalized. Assumed or estimated selection mechanisms permit sensitivity analysis of a meta-analysis, but unavailable results generally prevent a fully assumption-free correction.