That hairy caterpillar

Textbooks on Bayesian inference often refer to a ‘hairy caterpillar’ when describing the traceplot and what it should look like. It’s easy to come across examples what things look like, examples of this hairy caterpillar:

Likewise, we often see examples of the autocorrelation plot where everything is fine: a quick decrease to values around zero:

What seems less common are examples of what things should not look like, such as a traceplot that does not look like a ‘hairy caterpillar’ at all, or autocorrelation that really does not want to behave. Here I provide examples of both. How about this beauty, where each chain seems to be up to its own thing? This definitely does not look like convergence, nor do the chains mix well.

Or how about this trend? We need to stretch the definition of ‘quickly’ beyond any recognition to argue that this resembles a quick decrease.~

So yes, it’s back to the drawing board for this model… longer chains (with more thinning) may not suffice here.