Consider the example of hierarchical Bayesian analysis of the usual one-way ANOVA (Example 7.13 of the...

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Consider the example of hierarchical Bayesian analysis of the usual one-way ANOVA (Example 7.13 of the book by Ghosh et al. 2006, page 227) discussed in the class. Take k = 10 and n₂ = 25 for all i. Generate 10 samples, each of size 25, from 10 normal populations. Choose 10 different values of the pou- lation means 1₁,...,010 and a common value of the population variance. Choose the values of the hyperparameters a1, a2, b₁,b2, po, o so that the cor- responding priors are not very informative. Use the Gibbs sampling proce- dure to estimate the poulation means. Do the same for five different choices of (a1, a2, b1,b2, po, o). Do the above (a) using WinBUGS and also (b) using your own code written in your favourite programming language such as R or Python. Consider the example of hierarchical Bayesian analysis of the usual one-way ANOVA (Example 7.13 of the book by Ghosh et al. 2006, page 227) discussed in the class. Take k = 10 and n₂ = 25 for all i. Generate 10 samples, each of size 25, from 10 normal populations. Choose 10 different values of the pou- lation means 1₁,...,010 and a common value of the population variance. Choose the values of the hyperparameters a1, a2, b₁,b2, po, o so that the cor- responding priors are not very informative. Use the Gibbs sampling proce- dure to estimate the poulation means. Do the same for five different choices of (a1, a2, b1,b2, po, o). Do the above (a) using WinBUGS and also (b) using your own code written in your favourite programming language such as R or Python.

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