Is your model converging?

This post is by Aki

I too often see people saying their model is converging or not converging. Sure, if you are doing iterative model building as part of your Bayesian workflow you could say that that iterative process eventually converges to the final model, but it seems people are actually talking about whether the inference algorithm is converging.

A Bayesian model describes a joint distribution of data and parameters. If we condition on observed data, we get the posterior distribution. We often use iterative inference algorithms to make posterior inference. If the inference algorithm doesn’t converge, the convergence problems don’t depend only on the model, but on the model, parameterisation, and the data, which together determine the geometry of the posterior. The same model and different parameterisation or data lead to different posterior geometry. For the same posterior, different iterative algorithms or algorithm choices can also lead to different convergence problems. (We have several exmples of iterative inference algorithm convergence problems in the soon to appear Bayesian workflow book)

If you want someone to help with possible inference convergence problems, it is not sufficient to tell which model you have, but you also need to tell about the parameterisation, data, and algorithm. Stop talking about models (not) converging (unless doing iterative model building) and talk about the inference algorithm (not) converging, as it is more accurate and implies dependency on the posterior and algorithm.