I have a conceptual question. I’m wondering about scenarios where some variables that have a small number of effective samples are dependent of variables that have a large number of effective samples, and vice versa.
For example, let’s say variable A has a low number of effective samples, and variable A affects variable B. B has a high number of effective samples. Let’s say we only care about B. Even though B has a high number of effective samples, Is B going to be biased because it makes use of variable A?
How about the other scenario: B affects A’s value. Let’s say A has a high number of effective samples, but B doesn’t. Let’s say A is the parameter of interest. Is A likely to be biased because it listens to B, even though A has a high number of effective samples?
My personal take is that, if you are computing expectation of some function using the posterior samples, the bare minimal is that the samples that are going into the said function should be good (i.e., rhat and effective sample size are both good).
Thus in your case, when you have many variables and some with good effective sample size and some are not, usually focus on the variable that you are actually interested in is fine, as long as you carefully check. Some examples I can think of is transformed distributions. For example, when you are using von mises distribution, the transformed variable actually have horrible rhat and effective sample size (because it is circular).
So TL;dr is that, in most case you are fine regardless of the effective sample size from its dependence, but you should always carefully look at your model.
Yes, I only care about variables that have large number of effective samples & good rhat values. They are all beta distributions – probability of giving birth, survival, and detection for certain years, and nothing like the Von Mises distribution, so your response is reassuring. Thank you very much, @junpenglao!
Also, you should have a look at this post (especially Mike’s response in the thread) that discuss related convergence issue.
Thanks. Did you forget to post a link?