i Have been playing with VI for a while using a simple logistic regression test case. What I find is you can get very accurate results always using NUTS as long as you have enough input data. For VI on the other hand you get good results on the intercept and larger coefficients but an overestimate on smaller coefficients. The same is true actually with NUTS if insufficient data is given.
I have been wondering if there is some kind of reparamterization trick that will fix this small coefficient problem, but found nothing out there. Is inaccuracy simply an unavoidable fact when using VI?