Posterior Landscape (Arthur's Seat)
Show terrain
Posterior Density (Emerging from Exploration)
The Profound Point
With the terrain hidden, you see how MCMC discovers the posterior without knowing the landscape. The chains only know local information (can I go higher from here?) yet collectively map out the full distribution. This is how Bayesian inference works on problems we can't visualise.
Prior Distribution
Click on the terrain to position the prior ellipse
Prior Shape
MCMC Settings
Convergence Diagnostics
What is R-hat?
R-hat (Gelman-Rubin statistic) compares variance within chains to variance between chains. When chains converge to the same distribution:
- R-hat < 1.1 — Chains have converged
- 1.1 ≤ R-hat < 1.2 — Nearly converged
- R-hat ≥ 1.2 — Chains haven't converged yet
Traceplots (Log-posterior)
Watch for burn-in (initial climb) then stable mixing around high-probability regions
The Bayesian Perspective
In Bayesian inference, we don't just find the best parameter values — we explore the full posterior distribution. The posterior tells us which parameter values are plausible given our data.
We use log(elevation) as the log-posterior density: higher = more plausible parameters. This creates more realistic traceplot behaviour — watch for the initial "burn-in" climb as chains find high-probability regions, then stable mixing once they've converged.