 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/iii/paper-36/3/e/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

Delete the plate random effects from the linear predictor and remove their stochastic nodes and the unused scale/precision nodes. The observation layer then remains a Poisson distribution with

lo g μ_{ij} = α + β lo g (x_{i} + 10) + γ x_{i} .

For example the essential WinBUGS observation block can be written as

for (i in 1:doses) {
for (j in 1:plates) {
y[i,j] ~ dpois(mu[i,j])
log(mu[i,j]) <- alpha + beta*log(x[i]+10) + gamma*x[i]
}
}

Retain the coefficient priors. This is the

τ = 0

sampling model implemented directly; attempting to keep 1/(tau*tau) while fixing tau to zero would divide by zero.

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