gompertz_mcmc.py

import numpy
from theano import shared
import pymc3 as pm

x = np.arange(len(df))

# we set a shared tensor useful for inference
x_shared = shared(x)

y = df['totale_casi'].values

# This is the model created with PyMC3
with pm.Model() as model:
    
    # 'priors' distributions 

    par0 =  pm.Normal("par0", mu=2.6e+05, sigma=2.6e+03)
    par1 =  pm.Normal("par1", mu=1.2, sigma=1)
    par2 =  pm.Normal("par2", mu=0.6, sigma=1)
    par3 =  pm.Normal("par3", mu=3.2, sigma=5)

    gompertz = par0* np.exp(-par1*np.exp(-par2*(x_shared-par3)))
    
    eps = pm.HalfNormal("err")
    
    # The Likelihood
    pm.Lognormal("L_italia", np.log(gompertz), eps, observed=y)
    
    # MCMC
    trace = pm.sample(tune=2000, target_accept=0.99, chains=2)