# Convergence problems - discussion Current plan: - have this in the user's guide. - unite all warnings, then specific advice for divergences/treedepth/ESS/Rhat - Which suggestions are most useful for which type of warning? - Few divergences: increase adapt_delta - Short computation + treedepth: increase treedepth - Build on https://mc-stan.org/docs/2_26/reference-manual/divergent-transitions.html and https://mc-stan.org/misc/warnings.html - We'll want separate document on pre-runtime warnings - Source: https://github.com/stan-dev/stan-dev.github.io/blob/master/misc/warnings.Rmd - Additional reparametrizations to mention - "non-centering" other distributions than normal - QR decompostition / centering - Sum to zero constraint - Warnings are important, the goal is not to "make them go away" - Aki: - when we can ignore warnings. Some place for quick experiments - But with final model, you need to handle them! - Some problems are with posterior (not with model) - Maybe even posterior vs parametrization - degeneracy -> highly varying curvature (of the log) - mountain analogy maybe wrong - or discontinuous log-density - or floating point inaccuracies - normal distribution - constant curvature of the log (so not normal posterior is an issue) - remove "identifiability" -> likelihood is not informative - Reparametrization: anything else than draws from normal distribution is suspect (and then give examples) - Martin: Maybe a separate subsection for brms/rstanarm *** So you got: ``` Warning: There were XXXX divergent transitions after warmup. ``` What does it mean? What to do? Divergent transitions are a signal that there is some sort of degeneracy; along with high Rhat/low n_eff and "max treedepth exceeded" they are the basic tools for diagnosing problems with a model. Divergences almost always signal a problem and even a small number of divergences cannot be safely ignored. We should note that resolving modelling issues is generally hard and requires some understanding of probabilistic theory and Hamiltonian Monte-Carlo, see https://discourse.mc-stan.org/t/understanding-basics-of-bayesian-statistics-and-modelling/17243 for more general resources. ## What is a divergent transition? ## Hints to diagnose and resolve divergences What follows is a list of brief hints that could help you diagnose the source of degeneracies in your model - or at least let you get faster help here on forums. Where they exist, we link to additional resources for deeper understanding. The aim is to provide a birds-eye view of approaches we've had success with in the past, point you to additional resources and give you keywords to search for :-) This is not, and can't be a definitive guide - each degenerate posterior is problematic in its own way and there is no single approach that would always work. If you fail to diagnose/resolve the problem yourself or if you have trouble understanding or applying some of the hints, don't worry, you are welcome to ask here on Discourse, we'll try to help!