This exercise is concerned with two versions of the Bayes estimate of the seasonal rainfall component, where it is required to compute \(E\left(\eta_{m} \midight.\) data) for each of 12 months. As usual, \(\chi\) is the chordal distance as measured on the clock whose perimeter is 12 units, and month is a factor having 12 levels. In computer notation, the code for fitting the two models is as follows, where \(K=\) const \(-\chi\) is positivedefinite of order \(n \times n\) and rank 12:

Positive definiteness is not required for computation so the constant is immaterial, but \(K\) is positive definite if the constant exceeds \(2 \tau / \pi^{2}=24 / \pi^{2}\). Compute the Bayes estimate of monthly means for each model and superimpose these points on the plot of monthly averages.

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