How to include data measurement uncertainty in stan/pystan

Question

I am completely new to stan. I simply wanted to fit a data which has uncertainty in measurements, but I could not include the uncertainty in the fitting. For example, I have x[N], y[N] and yerror[N] arrays with dimension N. Suppose the data is 2nd order polynomial: y=a0+a1x+a2x*x, and I have the error in y, yerror[N]. Now my code in pystan is given below:

import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np

A0=0.5; A1=1.5; A2=-0.2; A3=-0.008; A4=0.00025
def func(xx):
    return A0+A1*xx+A2*xx*xx#+A3*(x**3)+A4*(x**4)

x=10*np.random.rand(100); x=np.sort(x)
fx=func(x);
yerror=np.random.rand(len(x))
y=np.random.normal(fx,scale=sigy)

np.random.seed(101)

model = """
data {
    int<lower=0> N;
    vector[N] x;
    vector[N] y;
}
parameters {
    real a0;
    real a1;
    real a2;
    real<lower=0> sigma;
}
model {
    vector[N] x2;
    for(i in 1:N){x2[i]=x[i]*x[i];}
    y ~ normal(a0 + a1 * x + a2 * x2, sigma);
}
"""

# Put our data in a dictionary
data = {'N': len(x), 'x': x, 'y': y}

# Compile the model
sm = pystan.StanModel(model_code=model)

# Train the model and generate samples
fit = sm.sampling(data=data, iter=2000, chains=4, warmup=400, thin=3, seed=101)

The code does not use the uncertainty in the data measurements, yerror[N]. How to do that? Sorry if I am asking something silly/answered already. Thanks in advance.

Answer 1

I found the answer from the following link. We have to change the "parameter" sigma to the known yerrors.