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[organization_capital] posterior-mean figure does not show the convergence the text describes #1015

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@Chihiro2000GitHub

In lectures/organization_capital.md, the cell producing the "Posterior mean convergence and uncertainty" figure simulates a single worker with T = 20. The text just below it says:

As the number of screening observations $n$ increases, the posterior mean converges to the true $\theta$, and the posterior uncertainty shrinks at rate $1/\sqrt{n}$.

The posterior mean in the left panel does not converge to θ_true = 0.8. It wanders and ends well away from it.

This is about the sample size rather than the seed: PR #1014 migrates the cell to np.random.default_rng(0), which changes the draws but not this behaviour. Screenshots of the figure before and after that migration are attached below.

Before the migration:

Image

After the migration:

Image

Two ways to make the figure match the text:

  1. Increase T.
  2. Or soften the prose so that it describes what the figure shows at T = 20.

CC @mmcky and @HumphreyYang.

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