How do you read a trace plot to determine when an MCMC chain has reached stationarity?

Conditions

• Used for diagnosing MCMC convergence.
• Requires plotting sample values against iteration numbers.
• The plot shows both the burn-in and stationary phases.

Reasoning, step by step

1. Plot the sample values against the iteration number.
2. Identify the initial phase where values are still converging (often shown in red).
3. Locate the transition point (e.g., a vertical dashed line) where the behavior changes.
4. Observe the subsequent phase where values fluctuate around the target distribution's equilibrium (often shown in green).
5. Conclude that the chain has reached stationarity after the transition point.

Example

The video shows a line graph plotting 'Value' against 'Iteration', with a red wavy line transitioning to a green wavy line after a vertical yellow dashed line at iteration 15.

Common misconceptions

• Assuming that a flat line in a trace plot always indicates good convergence, rather than potential lack of mixing.
• Believing that the trace plot alone is sufficient to prove convergence without other diagnostics.

Watch the explanation

Explore next

• What is the burn-in period in MCMC and why must those samples be discarded?
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• How does dependent sampling work in MCMC?