Summary
By reanalyzing a well known data set on the breaking strength and thickness of starch films, it is concluded that Fong's assumption of an exchangeable prior for the regression coefficients is correct but that the assumption of equal error variances might be wrong. This conclusion is made by calculating the Intrinsic Bayes factor for various models. The theory and results derived by Fong (1992) are therefore extended to the unequal variance case. This goal is achieved by implementing the Gibbs sampler. The vector of posterior probabilities thus obtained provides an easily understandable answer to the selection problem.
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Van der Merwe, A.J., Du Plessis, J.L. A Bayesian approach to selection and ranking procedures: the unequal variance case. Test 5, 357–377 (1996). https://doi.org/10.1007/BF02562623
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DOI: https://doi.org/10.1007/BF02562623