# Current shared-hypermean probabilities

These calculations post-process the cached six-component reference likelihood from the current fifteen-context, fourteen-likelihood-block autism hierarchy (5,133 cells). The estimand is the model's shared mean parameter, not a universal vaccine effect, an individual vaccinated-versus-unvaccinated contrast, or a probability that every effect is zero.

The latent grid parameter is a = μ + b, with shared bias b ~ Normal(0, 0.15²). For each continuous prior μ ~ Normal(0, s²), the marginal prior for a is Normal(0, s² + 0.15²), and μ conditional on a is integrated analytically. The six saved product/context heterogeneity components retain equal prior weight; their heterogeneity does not vanish when μ=0.

## Continuous shared-mean posterior

| Prior SD for μ (log RR) | Median shared RR (95% CrI) | P(μ<0) | P(μ>0) | P(RR>1.10) | P(within reciprocal 5% region) |
|---:|---:|---:|---:|---:|---:|
| 0.3466 | 0.968 (0.650–1.437) | 56.4% | 43.6% | 26.2% | 19.0% |
| 0.6931 | 0.957 (0.599–1.517) | 57.5% | 42.5% | 27.5% | 16.3% |
| 1.3863 (diagnostic only) | 0.953 (0.581–1.545) | 57.8% | 42.2% | 27.8% | 15.6% |

The full CSV reports protective / practical-null / positive probabilities at reciprocal margins RR 1.01, 1.02, 1.05, and 1.10 for every prior. The saved hierarchy's x0.5 and x2 sensitivity rows scale shared-bias SD along with μ-prior SD, while this suite holds it at 0.15. The x0.5 fixed-bias interval is 0.650–1.437 versus 0.675–1.373 in the cached jointly-scaled row; the x2 grid diagnostic is 0.581–1.545 versus the cached jointly-scaled interval 0.478–1.893. These are different prior specifications, not failed numerical replications.

## Point-null sensitivity

Here the point null is μ=0 only. Context/product heterogeneity remains active, and shared bias remains N(0, 0.15²). Bayes factors compare that model to a continuous Normal prior on μ; posterior null probabilities are shown for three prior null masses.

| Prior SD for μ | BF₀₁ (shared-mean null vs continuous) | Posterior P(μ=0), prior mass 20% | 50% | 80% |
|---:|---:|---:|---:|---:|
| 0.3466 | 1.708 | 29.9% | 63.1% | 87.2% |
| 0.6931 | 2.932 | 42.3% | 74.6% | 92.1% |
| 1.3863 — diagnostic only | 5.592 | 58.3% | 84.8% | 95.7% |

## Numerical checks and limits

The reference posterior reproduces the cached hierarchy median and interval; the reference minimum relevant core ESS in the saved model is 106.0. Half-grid quadrature reduces the latent grid from 241 to 121 points; the largest absolute difference in the reciprocal 5% ROPE probability is 5.03e-09, and the largest absolute difference in P(μ>0) is 2.79e-09.

The wider prior is shown only as a grid-based diagnostic: no prior-specific local core-ESS assessment was recomputed for this fixed-bias reweighting, so do not treat its tails or Bayes factor as fully validated. The saved JSON's x0.5/x2 sensitivity rows also rescale shared-bias SD with μ-prior SD, unlike this suite's fixed shared-bias SD of 0.15. Cached core-draw ESS does not automatically transfer across these likelihood weightings. Agreement under prior changes is not evidence against bias, nonidentification, selection, or misspecified exposure/outcome models. No conclusion here assigns a probability that every vaccine is harmless or that any individual risk is zero.

Source hashes are recorded in `mean_probabilities.json`. No input hierarchy JSON or manuscript source was modified.