Compare vensim and stanify

[hyunjimoon]

S = 30, M = 1000 (vensim and stan would be different but non-autocorrelated, converged sample), N = 20

without process noise, with measurement noise

1. Compare the average: prior_pred_obs: https://github.com/Data4DM/stanify/blob/main/stanify_demo.py#L47

Use alpha, beta, gamma, delta prior dist defined in draws2data stan file.

We assume stan's rng and vensim's rng is similar. In stan, prey_obs ~ normal_rng(prey, m_noise_scale)

array([ 0.24878059,  0.29612573,  0.55957889,  0.06677449, -2.04914881,
       -0.08381008, -0.82436614,  0.5243477 , -0.60570814, -0.37597002,
       -0.92898971,  0.0248358 ,  0.60356123, -0.75828866,  0.12360369,
        0.18310545, -0.37519184, -0.77519677,  0.07079331,  0.17829731])

Compare prey_obs, predator_obs

estimate for without process noise

with process noise, with measurement noise

Consistency of realized random variable should be matched. Lookup function (CDF) is the right way to go. make sure np.random.normal(0,1, size=n_t) is used

array([ 0.24878059,  0.29612573,  0.55957889,  0.06677449, -2.04914881,
       -0.08381008, -0.82436614,  0.5243477 , -0.60570814, -0.37597002,
       -0.92898971,  0.0248358 ,  0.60356123, -0.75828866,  0.12360369,
        0.18310545, -0.37519184, -0.77519677,  0.07079331,  0.17829731])

[hyunjimoon]

@tomfid updated result (uploaded in stanify repo); surprising process noise makes estimation stable.