Comparison of lots of data vs. not much data for a bad fit

badfit.py

#%%

import matplotlib.pyplot as plt
import pystan
import numpy

model_code = """
data {
  int<lower=1> N; // Number of single samples
  vector[N] t;
  vector[N] y;
}

parameters {
  real<lower=0.0> sigma;
  real a;
  real b;
}

model {
  y ~ normal(a * t + b, sigma);
}
"""

sm = pystan.StanModel(model_code = model_code)

#%%
N = 100

x = numpy.linspace(0, 10.0, N)

y = x*x + 5.0 * numpy.random.randn(N)

plt.plot(y)
plt.show()

print "Not much data"
print sm.sampling({'N' : N, 't' : x, 'y' : y})

N = 10000

x = numpy.linspace(0, 10.0, N)

y = x*x + 5.0 * numpy.random.randn(N)

plt.plot(y)
plt.show()

print "Lots of data"
print sm.sampling({'N' : N, 't' : x, 'y' : y})