Bayesian Update - Interactive Demo

Click "Run" in the sidebar to update plots. All calculations are done within browser.

Description

This Demo shows a progress in real-time :

  • A progress of posterior mean converges into the true value
  • 95% HDI (sampling based)
  • Posterior predictive (sampling) distribution histogram
  • Assess convergence speed by checking KL divergence(true || posterior-mean)

Let's see how the prior belief converges along the updates.
Ex1 - You have a die of six faces. You have a prior belief that 1 comes out 50%, rest 10% each. If the die is actually fair(1/6 each), how many trials we need to see the convergnece?
Ex2 - There is a bus coming every 30 minutes. Your experience tells that you normally wait under 5 minutes 4 times out of 10.
Ex3 - A weekly lottery has winning rate of 0.1%. If you buy one lottery every week, what would be the probability of winning at the 7th week for the first time?
Ex4 - Two players, A and B, are playing game; A has a 70% chance of winning against B. You believe that it is not 70%, but 30%. Then what would be the posterior probability of the match ends at 5th game?
Ex5 - Current quality assurance system takes 20 months to see the first defective product. Your prior belief follows gamma distribution of alpha=1, beta=6. What would be the convergence look like, if the actual prodcution quality follows gamma distribution of alpha=2, beta=4?