WEBVTT

NOTE Four roads to one posterior: captions match the on-screen steps.

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Step 1 of 8. The question: seven doses, ten patients each. Does a bigger dose help?

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Step 2 of 8. The explorer: the model every method fits, logit p = β₀ + β₁·dose with a flat prior.

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Step 3 of 8. Laplace, Metropolis-Hastings, HMC and EP run in Web Workers at seed 90125: R-identical.

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Step 4 of 8. Marginal posteriors of the dose slope β₁: four roads, one shape.

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Step 5 of 8. Means, sds, 95% intervals and ESS side by side: Laplace sits slightly low.

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Step 6 of 8. Settings: change the seed to 2026 and rerun all four methods.

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Step 7 of 8. New seed, same answer: the samplers move only by Monte Carlo error.

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Step 8 of 8. Joint posterior against the exact contours, and the implied dose-response curve.