Teaching Bayesian Model Comparison With the Three-Sided Coin

This article introduces the problem of determining the probability that a rotating and bouncing cylinder (i.e., flipped coin) will land and come to rest on its edge. We present this problem and analysis as a practical, nontrivial example to introduce the reader to Bayesian model comparison. Several...

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Bibliographic Details
Published in:The American statistician 2007-08, Vol.61 (3), p.239-244
Main Authors: Kuindersma, Scott R, Blais, Brian S
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian networks
Center of mass
Comparative analysis
Cylinders
Data models
Energy value
Exact sciences and technology
General topics
Log-likelihood
Marginalization
Mathematics
Mathematics education
Modeling
Occam's razor
Parameter estimation
Parametric models
Probabilities
Probability
Probability and statistics
Probability theory
Sciences and techniques of general use
Statistical analysis
Statistics
Surface areas
Teacher's Corner
Teaching methods
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Description
Summary:This article introduces the problem of determining the probability that a rotating and bouncing cylinder (i.e., flipped coin) will land and come to rest on its edge. We present this problem and analysis as a practical, nontrivial example to introduce the reader to Bayesian model comparison. Several models are presented, each of which take into consideration different physical aspects of the problem and the relative effects on the edge landing probability. The Bayesian formulation of model comparison is then used to compare the models and their predictive agreement with data from hand-flipped cylinders of several sizes.
ISSN:0003-1305
1537-2731
DOI:10.1198/000313007X222497