From sampling statement to distribution statement

The sampling statement name for tilde (~) statements in Stan documentation has been replaced with distribution statement. The background is

• the tilde (~) statement does not do any sampling (but due to the sampling statement name, some people had wrongly assumed so, which caused confusion)
• in the literature, tilde (~) is usually read “is distributed as”
• right side of the tilde (~) statement can only be a built-in or user defined distribution
• distribution statement makes it more natural to discuss the difference in defining the model with collection of distributions or with log density increments

The change affects only the documentation. The documentation has been revised to be more clear on differences in describing models with distribution statements and increment log density (target +=) statements.

As this blog lacks equations support, it’s best to go to read the updated documentation on distribution statement.

In addition, Stan User’s Guide sections on censored data models and zero-inflated count models are good examples illustrating the difference between describing a data model with distribution statement or writing the likelihood directly with increment log density statement.