Thanks a lot for good suggestions. But at least I got quite confused.

Population PK model may be simplistically expressed as a two level

hierarchical model:

y_it~normal(f(theta_i,t),sigma)

theta_i~normal(theta,tau)

where y_it - plasma concentration for individual i at time t

f - system of ODEs

theta - population parameter

At leas the system of ODEs I have (PBPK) model gives a very good fit -

as verified by predictive posterior - but gives bunch of divergencies.

theta is in reality vector for which some parameters have literature

values while some don’t. Thus I used quite vague prior for those which

don’t and informative prior for those which do.

Then I reparametrized the model:

y_it~normal(f(theta+ksi_i*tau,t),sigma)

ksi_i~normal(0,1)

and ran 4 chains. 3 chains showed a very good mixing but one chain was

like pig tail and was visibly outside the region defined by well mixed

chains. Well mixed chains didn’t have any divergencies but pig tail

chain had a lot of divergencies. Also, well mixed chains didn’t have any

normal_log: Location parameter[238] is 1.#QNAN, but must be finite!

errors after warmup but pig tail chain had them up to the end of

simulation. Those I guess were caused by function f giving nans for

nonsensical parameter values.

Then I did one more experiment - hard constrained parameters based on

ranges as determined from centered parametrization (first model). As a

result there were no divergenciens, perfect mixing etc. However, as I

understand hard constrains are not recommended. But I don’t know other

way how to remove pig tails (except ignoring them).

One more possibility for divergencies might be a very strong correlation

between parameters but it seems this correlation doesn’t cause

divergencies for non centered parametrization (second model).

Second model is attached. I appreciate any feedback. It runs for 5 days

(even when jacobian is supplied to CmdStan, thanks to Sebastian). By the

way, pig tail chain occurred for ncp model when jacobian was not

supplied.

Linas

pbpkauto.stan (11.5 KB)