For the model with persistent aviary patterns described at the end of Sect. 5.4.2, compute and plot the REML profile \(\log\) likelihood for \(\tau\) in the range \(0.5 \leq \tau \leq 24\). Use PC1 as the response, and (5.2) for the mean-value subspace. The covariance should be a linear combination of five matrices, one each for the identity matrix and the identity restricted to baseline, two Brownian-motion product matrices as in (5.4), and one \(\tau\)-shifted B-M product matrix. Ten to twelve points equally spaced on the log scale should suffice for plotting.