MCMC Sampling

Statistics • Bayesian Inference

Watch algorithms approximate complex probability distributions. Compare random walk Markov Chains to gradient-based Variational optimization.

1. Target Posterior

2. Algorithm

3. Animation SpeedMedium

Playback speed of the simulation.

4. Posterior Ruggedness0.0

Adds noise/local traps to the landscape.

5. Max Steps∞

Pause sampling automatically after N steps.

6. Setup Hyperparameters

Total Steps: 0

Global Acceptance: 0%

Proposal Step Size (σ)0.80

Variance of the random jump.

Number of Walkers3

Simultaneous chains. Great for local maxima.

Metropolis-Hastings Walkers propose a random jump. If the new location is denser, they always jump. If less dense, they jump *sometimes*. Black Contours: 1 (Solid), 2 (Dashed), and 3-sigma (Dotted) target boundaries. | Blue Heatmap: Sampled posterior. | Dotted Lines: Rejected jumps.