= Solution
The PDF output places $-1$ inside the 95% <credible interval> for the time slope, whose endpoints are approximately $-1.329$ and $-0.7955$, and places $1$ inside the baseline slope interval, approximately $0.7915$ to $1.231$. Relative to their posterior standard deviations, the proposed fixed values are only
$$
\frac{-1-(-1.064)}{0.1352}\approx0.47,\qquad
\frac{1-1.023}{0.1145}\approx-0.20
$$
from the posterior means. Thus \b[the simpler choice $\beta=-1,\gamma=1$ is compatible with the fitted coefficient summaries] and has a natural proportional-decay interpretation. It is a reasonable constrained model to compare, not proof of the exact equalities: separate marginal intervals do not establish a joint constraint, and a continuous <posterior distribution> assigns a specified point probability zero.
The reported <Monte Carlo errors> measure numerical uncertainty in the estimated posterior means, not uncertainty about the coefficients themselves. In particular, the baseline slope's Monte Carlo error is about 9% of its posterior standard deviation, appreciably larger than the corresponding proportion for the time slope. Longer or better-mixed chains may be needed for precise summaries.
Back to article page