For the Oxford rainfall data up to Dec 2019, the first Bayes estimate in the preceding exercise is a flat \(10 \%\) shrinkage of monthly averages towards the annual average; the second Bayes estimate is different. For example, the average rainfall for September is \(55.6 \mathrm{~mm}\), which is slightly above the overall average of 54.7 , so the first Bayes estimate is \(55.5 \mathrm{~mm}\). The second Bayes estimate is \(57.5 \mathrm{~mm}\). Explain this phenomenon—why the September component, which is already above the annual average, is shifted even further from the overall average.