I am making a model for multicompartment pharmacokinetics. I am interested in more complex models, but I am having trouble formulating even simple ones in a way that pymc3 is happy with. The basic model is like this:
At every timepoint,
k01 x c0 mass flows from compartment 0 to compartment 1,
k10 x c1 mass flows from compartment 1 to compartment 0, and
u x c0 mass is excreted (destroyed).
I know that there are closed form solutions to this kind of model, but I am interested in more complex behavior, such as injections of mass at arbitrary times, where there are not closed-form solutions for
Therefore, my plan was to use a stochastic matrix to build a vector of concentrations over time, since
c*K[t] = c[t+1]
Here’s the code:
tsteps = 10 tobs = np.arange(tsteps) yobs = np.exp(-tobs/10) + np.random.normal(scale=0.1) with pm.Model() as model: theta = pm.Uniform('theta', lower=0, upper=1, shape=(3,)) k01, k10, u = theta, theta, theta K = tt.stack([tt.stack([1 - k01 - u, k01]), tt.stack([ k10, 1 - k10])]) c = [[1, 0]] + [None]*(len(tobs)-1) for t in tobs[1:]: c[t] = tt.dot(c[t-1], K) c = tt.stack([c[t] for t in tobs]) obs = pm.Normal("obs", mu=c[:, 0], sigma=0.1, observed=yobs) idata = pm.sample(1000)
This works well for
tsteps < 20, but hangs before even starting to sample for
tsteps = 30.
I strongly suspect that I am doing something (or several somethings) wrong here (for instance, the creation of lists that are then casted to theano tensors seems bad, for instance), but I’m not sure what to do differently.
Any advice would be appreciated!