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Bayesian multiple comparisons and model selection

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The testing of multiple hypotheses is an important consideration in many statistical analyses. A theme for multiple comparisons problems under a frequentist paradigm is the need for an adjustment to control the overall error probability for the false detection of null effects. Our review will focus on Bayesian approaches to multiple comparisons problems. Under a Bayesian paradigm, multiplicity adjustments arise from a concern that many of the effects to be tested are null. We will discuss how Bayesian models provide a multiplicity adjustment through a prior placing increased probability on null effects, or through hierarchical modeling. We will also show how the Bayesian information criterion for model selection fits naturally into the study of multiple comparisons problems. WIREs Comput Stat 2018, 10:e1420. doi: 10.1002/wics.1420

This article is categorized under:

  • Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory
  • Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
  • Data: Types and Structure > Traditional Statistical Data
Differences in the log‐transformed creatine kinase (CK) levels for 31 college football players. Differences reflect the increases in CK levels from the outset of training camp until one week into the camp.
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Estimated mean differences in the stress test scores. (1) corresponds to empirical group means; (2) corresponds to estimated group means under Bayesian model averaging; (3) corresponds to estimated group means under the highest posterior probability model (μom = μof, μym = μyf).
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Differences in the stress test scores for 35 cardiac rehabilitation patients. Positive differences reflect the increases in scores from the outset of the rehabilitation program to the end of the program.
[ Normal View | Magnified View ]
Estimated mean differences in the log‐transformed creatine kinase (CK) levels. (1) corresponds to empirical group means; (2) corresponds to estimated group means under Bayesian model averaging; (3) corresponds to estimated group means under the highest posterior probability model (μi, μf = μu).
[ Normal View | Magnified View ]

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