In Example 5.6 (popularity data), and retaining separate univariate normal priors (i.e. model 1) on the cluster

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In Example 5.6 (popularity data), and retaining separate univariate normal priors (i.e. model 1) on the cluster effects at stage 2 , assess the impact on inferences, such as on posterior means of \(\left\{\sigma, \tau_{1}, \tau_{2}, \tau_{3}\right\}\), of adopting uniform priors on the shrinkage parameters \(\sigma^{2} /\left(\sigma^{2}+\tau_{p}^{2}\right)\).

Data from Example 5.6

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