Hi to everybody.
I would like to ask you an opinion, or maybe if know the answer it is better.
I am fitting a 5 age-groups model of 7 differential equations for each group, that is 35 odes system.
I have also 25 parameters to be estimated.
I am using integrate_ode_rk45 to solve the system, with: rel_tol = 1e-4, abs_tol = 1e-4, max_num_steps = 5000 .
I am running 4 chains: 500 iterations (250 warm-up, 250 sampling).
Chain 1 took 0.275 seconds for gradient evaluation, Chain 2 took 0.349 seconds, Chain 3 took 0.471 seconds and Chain 4 took 0.419 seconds.
I have observed that after 40 minutes we are in this situation:
Chain 1: 110 / 500 [ 22%] (Warmup)
Chain 2: 106 / 500 [ 21%] (Warmup)
Chain 3: 40 / 500 [ 8%] (Warmup)
Chain 4: 71 / 500 [ 14%] (Warmup)
I would like to understand why there is this large difference between Chain 3, Chain 4, Chain 2, Chain 1.
I want to stess that it is not true it depends only from the gradien evaluation, it happened this scenario with a latecomer chain, which took less time for the gradient evaluation respect to the others.
In my opinion it means that the Hamiltonian function is located in a bad region, however I don’t have idea to help it.
Moreover I set the initial values with a function, but these initial values are given with complete randomness. Could be this the problem?
Each suggestions or opinion could be very useful and interesting.