Poisson autoregressive model PAR(1) gives E-BFMI warning

Modeling
2 
           mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat
phi        0.89  2.8e-3   0.03   0.83   0.87   0.89   0.91   0.94     99   1.04
c         50.34  8.7e-3   0.58  49.15  49.98  50.36  50.73  51.45   4520    1.0
lognoise   0.55    0.02   0.13   0.29   0.46   0.55   0.65   0.79     49   1.09
...
tau      9.2e-3  2.8e-4 2.7e-3 5.4e-3 7.4e-3 8.8e-3   0.01   0.02     91   1.04
noise      1.75    0.03   0.23   1.33   1.58   1.74   1.91   2.21     52   1.09
lp__      1.5e5    17.9 123.44  1.5e5  1.5e5  1.5e5  1.5e5  1.5e5     48   1.09

Some of the output in the first model aren’t mixing well. Large Rhat and low ESS. Rhat < 1.01 is the rule of thumb from [1903.08008] Rank-normalization, folding, and localization: An improved $\widehat{R}$ for assessing convergence of MCMC (which is a cool paper for the plots).

Looking at the model, the truncation on the phi prior should match the constraints on the phi variable itself. So like this:

real<lower = 0.0, upper = 100.0> phi;

I think you should do a non-centering on the AR(1) process. I’m not sure how to do that offhand cause of the lower = 0 constraint, but you can try following along here: Non-centered parameterisation with boundaries - #5 by Bob_Carpenter .

It would probably be easiest to not have the constraint though.

1 Like