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Your Hierarchical Model Reports R-hat 1.3 and 18 Effective Samples: What Now?
You fit a hierarchical conversion model in PyMC with 4 chains of 1,000
draws. The summary shows, for the group-level spread parameter
\sigma, r_hat = 1.30 and ess_bulk = 18, and the sampler warned of
41 divergences. A teammate says "the posterior means look sensible,
let's ship the dashboard".
- Explain what R-hat and ESS measure and why these values mean the results cannot be used.
- List the diagnostics you would inspect next and what each could reveal.
- Give a prioritised list of fixes, including the reparameterisation that usually cures hierarchical divergences.
- What would you show to demonstrate to the teammate that "sensible means" are not enough?
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