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Center the log-time predictor and the baseline log measurement near their sample means, so the intercept describes a typical predictor configuration. This reduces intercept-slope posterior correlation and can improve Markov chain Monte Carlo mixing. If exactly the original model is required, transform the intercept prior consistently when changing coordinates rather than silently assigning a different independent prior.

For weakly informed child effects, a non-centered Gaussian random-effect parameterization can also help:This retains the same conditional prior distribution for ${\alpha }_i$ but removes its prior-scale dependence from the sampled $z_i$. It can reduce strong dependence between the effects and $\tau$. A centered parameterization can be better when each child's effect is very accurately observed, so improvement is not automatic. Blocking strongly correlated coefficients is another option. Check the resulting chains with Markov chain Monte Carlo convergence diagnostics and effective sample size of a Markov chain, rather than judging convergence from the number of iterations alone.