BUGS

BUGS specifies a probabilistic model through stochastic nodes, deterministic nodes and observed data, then uses Markov chain Monte Carlo to simulate its Bayesian posterior. Its normal sampling notation uses a precision parameter rather than a variance, and its gamma notation uses shape and rate.

A zeros trick implements a positive likelihood function $L(\theta )$ by adding an observed zero with Poisson distribution mean $K-\log L(\theta )$. If this mean is nonnegative throughout the parameter support, its likelihood is $e^{-K}L(\theta )$ and yields the intended Bayesian posterior. The constant $K$ must be independent of the parameter; arbitrary clipping changes the target.