Model Fitting with "Bayesian Methods".md

FITTING A MODEL WITH THE LIBRARY "Bayesian-Methods"

STEP 1: import libraries.

import pymc as pm
import corner
import numpy as np
import arviz as az
from pymc.distributions.transforms import Interval

The last line is only needed for some of the codes

STEP 2: setup the code for running.

For this example, we fit the model from chapter 6.1.2. First of all, we need to read the data:

(obstot, obsbkg, C) = np.loadtxt('/Dataset/data6.1.2.dat', delimiter = ",", unpack = True)

The full model is specified in the library:

with pm.Model() as model:
  pm.Uniform("s", lower = 0, upper = 1.0e7)
  pm.Uniform("bkg", lower = 0, upper = 1.0e7)
  pm.Poisson("obstot", mu = (model['s'] + model['bkg']/C), observed = obstot)
  pm.Poisson("obsbkg", mu = model['bkg'], observed = obsbkg)

Step 3: run the sampler.

To sample the posterior distributions we use this instruction:

chain = pm.sample(return_inferencedata = True)

Step 4 (optional): plot and summarize.

To get a summary of the posterior you can use:

print(az.summary(chain.posterior['s']))
print(az.summary(chain.posterior['bkg']))

To draw a plot of the posterior you can use:

figure = corner.corner(chain.posterior['s'][0])
figure = corner.corner(chain.posterior['bkg'][0])