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feat: add a VAR-aware convergence and stability report #142

Description

@thomaspinder

What to build

Provide one report that surfaces sampler failures in VAR-shaped posteriors instead of requiring users to inspect hundreds of scalar rows. It should aggregate rank-normalised split-Rhat, bulk and tail ESS, and divergences by parameter block, then add the VAR-specific stability check ArviZ cannot supply: the posterior distribution of the companion-matrix spectral radius and the probability of explosive dynamics. Integrate the output into the diagnostics tutorial tracked by #57 without duplicating predictive simulation tracked by #56.

Acceptance criteria

  • The report summarises Rhat and ESS by coefficient, intercept, covariance, volatility, and applicable identification blocks while retaining the worst offending coordinates.
  • It reports the posterior spectral-radius distribution, explosive-draw probability, and a clear warning for the high-Rhat/zero-divergence and unstable-draw failure modes.
  • Synthetic healthy, non-converged, and partly explosive posteriors validate the classifications, and Add tutorial notebook: diagnosing fit in an Impulso VAR #57 documents how to interpret and act on the report.

Blocked by

None - coordinates with #56 and #57 but can start immediately.

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    documentationImprovements or additions to documentationenhancementNew feature or requestready-for-agentFully specified, AFK-ready

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