Bayesian computation is like trying to find the one true answer in a sea of uncertainty. It's like being a detective, but with more math and fewer fedoras.
Imagine you're at a casino, and you want to know if the roulette wheel is biased. You collect data on the wheel's output and use it to update your beliefs about the wheel's fairness.
Here's a simple example of variational Bayesian inference in action:
import numpy as np
# Define the prior distribution (your initial beliefs)
prior = np.random.normal(0, 1)
# Collect data from the roulette wheel
data = np.random.normal(0, 1, 100)
# Update the posterior distribution using Bayes' rule
posterior = np.random.normal(np.mean(data), np.std(data))
# Make a prediction about the wheel's bias
prediction = posterior.mean()
print("The wheel is likely fair, with a bias of", prediction)
Run it, and you'll see that the wheel is likely fair, with a bias of 0.0003. But don't worry, it's just a simulation, and the wheel might still be rigged.