Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-44/4/h/solution
Past exam of the mathematics course of the University of Cambridge 2008 iii Paper 44 4 h Solution by
Codex 0 2026-10-14
Model A has fifteen separate curve parameters plus one error-scale parameter. With such broad priors, one might have expected more of those sixteen parameters to be effectively estimated, rather than , and might also have expected its greater unpooled flexibility to give better fit than the displayed . Model B instead has a smaller mean deviance despite sharing information between trees.
This is a diagnostic concern, not a mathematical impossibility. Effective parameter count in DIC depends on posterior curvature and parameterization, while mean posterior deviance is not minimized deviance. A weakly identified nonlinear asymptote–slope trade-off, skewness, multiple posterior regions or slow Markov chain Monte Carlo mixing could explain the unexpected comparison. For A, the implied deviance at the posterior mean is ; for B it is . Inspect traces, effective sample sizes, independent chains and fitted curves, and extend sampling where needed. Fifty thousand iterations alone do not establish convergence.
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