I am modeling annual densities of birds to estimate population trends in a Bayesian framework, using a log-link regression in rjags. I am modeling long term (2002 - 2020) and short term (2011-2020) time periods. I have done this successfully for other species in the same system, but one species in one period of time (short term) is not converging. I think this is because the density for the first year is an outlier (in this case in year 2011 for the short term analysis); it is much higher than the other data (see figure). I am thinking the convergence failure is because this outlier is affecting the alpha (intercept) parameter during the MCMC process. Am I on the right track? I've attached a graphic of a successful estimation of the long term population trend (2003-2020) using the same analytical process. I also added in the unsuccessful estimation of the short term population trend. I've also included my code, and graphics of trace plots. In the trend graph, you can ignore the barplot and the right side y axis, which indicate precipitation.
Dear Brian Leo
Take a look: https://community.rstudio.com/t/jags-why-my-bayesian-model-fails-to-converge/56398
Kind Regards
Qamar Ul Islam
Without looking super closely I can see that you have crazy wide priors on alpha and beta. Both of those are exponentiated and so if there is any probability density near exp(beta)=0 (same for alpha) then all values of say -Inf < beta < -2 will be equivalent b/c exp(-20) and exp(-30) are numerically the same (0). So you've got a really flat posterior which is why those chains "wander" in that space -- there is no information in either the prior or data to differentiate them.
Tighten up your priors on both parameters so they naturally truncated really large negative numbers, and have a positive number that makes sense to you. There are examples around and also see: https://betanalpha.github.io/assets/case_studies/prior_modeling.html for some general advice on how to think about setting priors. I.e. your prior pushforward distributions would be piled up at 0.
Presumably your other data situations had a stronger signal to that exp(beta) and exp(alpha) >0.
I agree with Cole C Monnahan about the width of the priors, these likely need to be tightened up a lot. Another good reading on this topic is here:Article Visualization in Bayesian Workflow
.The outlier will affect the estimates of alpha and beta, but I think it is unlikely it affects the MCMC convergence. You can always try removing the outlier.
Another option you could try is to standardise the time trend variable by dividing (Year[i]-2016) by the standard deviation of Year[1:T].
Check https://agabrioblog.onrender.com/tutorial/glm2-jags/glm2-jags/
Also check https://stats.stackexchange.com/questions/556181/bayesian-log-link-regression-fails-to-converge-using-rjags-in-r
https://cchecastaldo.github.io/BayesianShortCourse/content/lectures/JAGSPrimerMCMCVis.pdf
Kindly check on this paper
Article Log-binomial models: Exploring failed convergence
Thanks Cole C Monnahan I tightened both priors substantially and my parameter means now make much more sense -- but the trace plot still doesn't look as good as some of the others. I'll have to dig into all of these suggested readings to determine more formal diagnostics, if any. I'm also not certain how to write up/justify my manipulation of the prior, which is now more informative.
You might just have to run it a little longer, and that's OK. Some models are harder to integrate than others. Regarding justifying this, use the concepts in the papers about implied priors (pushforward priors) and how these make more sense to you a priori. E.g., you can't have a trillion birds per km^2. If your prior model suggests that, then your priors are wrong. Find a range of densities you find plausible but wide, then tune your priors to get those. That's encoding your prior beliefs in the model. Betancourt shows this really well.
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