How to get a non-trainable random variable?

Questions v3
5 
import pymc3 as pm
import arviz as az
import numpy as np
import matplotlib.pyplot as plt
from pymc3.step_methods.arraystep import BlockedStep

class UpdateIndependentNoiseTermStep(BlockedStep):

    def __init__(self, epsilon, sigma, model=None):
        pm.modelcontext(model)
        self.vars = [epsilon]
        self.epsilon = epsilon
        self.sigma = sigma
        pass

    def step(self, point: dict): 
        sigma = self.sigma
        if not isinstance(1.0*self.sigma, float):
            sigma = np.exp(point[self.sigma.transformed.name])
            pass
        point[self.epsilon.name] = pm.Normal.dist(mu=0, sigma=sigma).random()
        return point
    
    pass

import pymc3 as pm
import arviz as az
import numpy as np
import matplotlib.pyplot as plt
from pymc3.step_methods.arraystep import BlockedStep
from custom import UpdateIndependentNoiseTermStep

data = 100 * np.exp(1) ** pm.Normal.dist(mu=0, sigma=0.2).random(size=2000)
plt.plot(data)

d1

with pm.Model() as model:
    alpha = pm.Normal(r"$\alpha$", mu=100, sigma=10)
    sigma = pm.HalfStudentT(r"$\sigma$", nu=3, sigma=0.15)
    epsilon = pm.Normal(r"$\varepsilon$", mu=0.0, sigma=sigma)
    update_fake_step = UpdateIndependentNoiseTermStep(epsilon=epsilon, sigma=sigma)
    alpha_eps = pm.Deterministic(r"$\alpha_{\varepsilon}$", alpha * np.exp(1) ** epsilon)
    obs = pm.Normal("obs", mu=alpha_eps, sigma=1, observed=data)
    step = pm.Metropolis(vars=[alpha, sigma])
    trace = pm.sample(4000, cores=4, chains=4, tune=10000, step=[step, update_fake_step], init='advi', return_inferencedata=True)
    pass

az.plot_trace(trace)

d2

az.summary(trace)
mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
𝛼 102.131 5.782 90.983 113.800 0.244 0.174 607.0 756.0 1.01
πœ€ 0.002 0.273 -0.422 0.449 0.002 0.004 15976.0 4481.0 1.00
𝜎 0.171 0.218 0.000 0.445 0.006 0.004 1251.0 1517.0 1.00
π›Όπœ€ 108.864 142.697 61.872 152.625 1.751 1.238 9790.0 4724.0 1.00

Roughly like this.

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