Problem with dynamically generating random variables in a Compound Poisson model

Questions v5
1

I am trying to build a model to estimate the parameters of a Compound Poisson process with a Binomial distribution as the underlying distribution. The process Y(t) is defined as: Y(t) = \sum_{m=1}^{N(t)}{Z_m}, where Z_m ~ i.i.d. Binom(n0, p0) and N(t) ~ Poisson(\lambda*t). From this definition, one can see that the number of Z_m’s is variable and has to be dynamically set based on N(t). I have come up with this basic framework, but am having trouble with dynamically setting the shape of pm.Binomial.

import numpy as np
import pymc as pm
import matplotlib.pyplot as plt

def sampling(data):
    """
    Markov Chain Monte Carlo estimation of the Compound Poisson process
    """
    with pm.Model() as cp_model:
        # Priors
        rate = pm.Gamma('rate', alpha=1, beta=1)
        n0 = pm.Gamma('n0', alpha=5, beta=1)
        p0 = pm.Beta('p0', alpha=2, beta=2)
        n_t = pm.Poisson.dist(mu=rate)
        trunc_n_t = pm.Truncated('trunc_n_t', n_t, lower=1)

        n_t_draw = pm.draw(trunc_n_t)
        print(n_t_draw)

        z_m = pm.Binomial('z_m', n=n0, p=p0, shape=(n_t_draw,))

        # Likelihood
        y_t = pm.Deterministic('y_t', pm.math.sum(z_m))
        likelihood = pm.Normal('likelihood', mu=y_t, observed=data)
    
    with cp_model:
        trace = pm.sample(
            draws=30000, 
            chains=4, 
            tune=1000, 
            step=pm.Metropolis(),
            cores=2
        )

    res = pm.summary(trace)
    print(res)

    pm.plot_trace(trace, rug=False, divergences=None)
    plt.tight_layout()
    plt.show()

    return res

I tried to use pm.draw to set the shape of pm.Binomial, but from the summary table and plot trace, the shape seems to be set on model definition instead of dynamically changed during training. Any help would be appreciated, thanks!