Bayesian Theory

We can implement Bayesian probability using Python. For our demo, we generate output values from two independent variables, x1 and x2. The output model is defined as follows:

c is a random value. We define α, β1, β2, and σ as 0.5, 1, 2.5, and 0.5.

These independent variables are generated using a random object from the NumPy library. After that, we compute the model with these variables.

We can implement this case with the following scripts:

import matplotlib
matplotlib.use('Agg')
import numpy as np
import matplotlib.pyplot as plt
# initialization
np.random.seed(100)
alpha, sigma = 0.5, 0.5
beta = [1, 2.5]
size = 100

# Predictor variable
X1 = np.random.randn(size)
X2 = np.random.randn(size) * 0.37
# Simulate outcome variable
Y = alpha + beta[0]*X1 + beta[1]*X2 + np.random.randn(size)*sigma
fig, ax = plt.subplots(1, 2, sharex=True, figsize=(10, 4))
fig.subplots_adjust(bottom=0.15, left=0.1)
ax[0].scatter(X1, Y)
ax[1].scatter(X2, Y)
ax[0].set_ylabel('Y')
ax[0].set_xlabel('X1...