Data are available on new daily age-specific COVID-19 mortality counts for a given country. The hierarchical model at hand models the age-specific latent transmission dynamics with an age-structured SEIR compartmental model. The estimated age-specific new daily infections are linked via some function with the age-specific expected daily deaths and those in turn are linked with the observed deaths via an over-dispersed count model. The age-specific force of infection is allowed to vary in time. See here and here for related models.
I have successfully fitted the hierarchical model using Rstan on a Windows desktop machine to data for a given country, where I assume that the population is split into three age groups (see image below), for a time series of 7 months.
The 7-month analysis model takes about 1.5 day to run (6 chains, 500 warmup iters + 500 main iters per chain). I use the Trapezoidal rule to solve the system of ODEs that represents the SEIR comartmental model which involves A^2 + 1 parameters for which appropriate prior distributions are assumed.
For external validation purposes I wish to reimplement the analysis for a further 3 months (10 in total). The 10-month analysis model takes about 3 days and, unfortunately, fails to converge, i.e. flat traceplots, \hat{R} are unreasonably large, n_eff is either 1.5 or 3 or 5 for all parameters.
Over the course of 2 months I have attempted to fine-tune my model with different prior distributions where appropriate. I use the point estimates from maximization of the joint posterior [optimizing() function] as starting values for the sampler. Unfortunately, all my attempts lead non-convergence and the execution times are prohibitively long.
What are the best practices to spot convergence issues as early as possible during sampling, so that the process can be terminated without having to wait for some many days?
Thanks.
GR_Experiment63_ModelFit.pdf (70.9 KB)