= Solution
Use <conditional versus marginal posterior predictive checks> to replicate new plates, rather than recycling the fitted plate effects. For each joint <posterior> draw of $(\alpha,\beta,\gamma,\tau)$, draw fresh independent $\lambda_{ij}^{\mathrm{rep}}\sim N(0,\tau^2)$ and then
$$
Y_{ij}^{\mathrm{rep}}\sim\operatorname{Poisson}
\left(\exp\{\alpha+\beta\log(x_i+10)+\gamma x_i+\lambda_{ij}^{\mathrm{rep}}\}\right).
$$
Use the same doses and three-plate design, giving the <posterior predictive distribution> for repeated experiments. Compare observed dose means and their trend, the high-dose downturn, within-dose spreads, and outliers with the replicated curves and intervals. For example compare a discrepancy
$$
T(y;\psi)=\sum_i\frac{(\overline y_i-m_i)^2}{[m_i+m_i^2(e^{\tau^2}-1)]/3},
\qquad m_i=e^{\eta_i+\tau^2/2},
$$
with $T(y^{\mathrm{rep}};\psi)$ draw by draw. The resulting posterior predictive tail fraction or graphical rank assesses whether the observed trend is unusual under this model. \b[Fresh plate effects are needed to assess the population dose-response assumption.] Reusing the fitted effects would mainly check the conditional sampling layer and could hide systematic departures from the proposed curve.
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