2007
DOI: 10.1007/s10463-007-0117-5
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Some remarks on Bayesian inference for one-way ANOVA models

Abstract: We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said differently, … Show more

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Cited by 4 publications
(5 citation statements)
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“…Alternatively, the p-values of the statistics may be reported and variables with p-value lower than a threshold level say 0.05 are selected as best candidate for further classification task (Hwang, Lee, and Park 2017). The classical one-way ANOVA method which authors like Guyon and Elisseeff (2003); Wright and Simon (2003); Qureshi, Oh, Min, Jo, and Lee (2017), among others used suffers from loss of information (Bertolino, Piccinato, and Racugno 1990;Solari, Liseo, and Sun 2008). Solari et al (2008) has worked on Bayesian one-way ANOVA as a safe haven to loss of information issue.…”
Section: Introductionmentioning
confidence: 99%
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“…Alternatively, the p-values of the statistics may be reported and variables with p-value lower than a threshold level say 0.05 are selected as best candidate for further classification task (Hwang, Lee, and Park 2017). The classical one-way ANOVA method which authors like Guyon and Elisseeff (2003); Wright and Simon (2003); Qureshi, Oh, Min, Jo, and Lee (2017), among others used suffers from loss of information (Bertolino, Piccinato, and Racugno 1990;Solari, Liseo, and Sun 2008). Solari et al (2008) has worked on Bayesian one-way ANOVA as a safe haven to loss of information issue.…”
Section: Introductionmentioning
confidence: 99%
“…The classical one-way ANOVA method which authors like Guyon and Elisseeff (2003); Wright and Simon (2003); Qureshi, Oh, Min, Jo, and Lee (2017), among others used suffers from loss of information (Bertolino, Piccinato, and Racugno 1990;Solari, Liseo, and Sun 2008). Solari et al (2008) has worked on Bayesian one-way ANOVA as a safe haven to loss of information issue. They suggested objective prior through Bayes factor as an alternative approach to handle one-way ANOVA model.…”
Section: Introductionmentioning
confidence: 99%
“…The effect‐estimation approach, on the other hand, provides a complete multi‐dimensional posterior estimate of all the parameters simultaneously, which can be meaningfully examined for any comparison of interest, as was exemplified earlier in Figure 5. Consider again the tomato acidity data from Ref 36. We can conduct a Bayesian ANOVA, and then compute a contrast in which the third group is compared with the mean of the other eight.…”
Section: Bayesian Data Analysismentioning
confidence: 99%
“…As an example, consider data reported in Table 3 of Solari et al 36 regarding an experiment that measured ascorbic acid content of tomatoes, in nine groups that were given different types of manuring. The third group appeared post hoc to differ from the other eight.…”
Section: Is There An Effect? Two Bayesian Approachesmentioning
confidence: 99%
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