Bayes learning simulation

- random variable x under Gaussian distribution
- u is unknown, σ is known
- p(x | u) ~ N(u, σσ)
- goal: guess u, the real mean, using Bayes parameter estimation

- assume p(u) ~ N(u0, σ0σ0)
- u0: our best guess for u
- σ0σ0: uncertainty about u0

- uN: best guess for u, given N samples
- σNσN: uncertainty about uN

experiment
- set u, u0, σ0 with random values
- at each frame...
　- N increases
　- simulate sample mean
　- calculate uN and σN
　- render our guess (red line is the real mean)

reference: Richard O. Duda. Chapter 3: MLE and Bayesian Estimation In Pattern Classification 2ed (pp. 11-13).