TY - JOUR
T1 - Connecting and Contrasting the Bayes Factor and a Modified ROPE Procedure for Testing Interval Null Hypotheses
AU - Liao, J. G.
AU - Midya, Vishal
AU - Berg, Arthur
N1 - Funding Information:
The authors are deeply grateful to the three anonymous reviewers, an associate editor, and editor Dr. Jeske for their expert guidance in the revision of the article.
Publisher Copyright:
© 2020 American Statistical Association.
PY - 2021
Y1 - 2021
N2 - There has been strong recent interest in testing interval null hypotheses for improved scientific inference. For example, Lakens et al. and Lakens and Harms use this approach to study if there is a prespecified meaningful treatment effect in gerontology and clinical trials, instead of a point null hypothesis of any effect. Two popular Bayesian approaches are available for interval null hypothesis testing. One is the standard Bayes factor and the other is the region of practical equivalence (ROPE) procedure championed by Kruschke and others over many years. This article connects key quantities in the two approaches, which in turn allow us to contrast two major differences between the approaches with substantial practical implications. The first is that the Bayes factor depends heavily on the prior specification while a modified ROPE procedure is very robust. The second difference is concerned with the statistical property when data are generated under a neutral parameter value on the common boundary of competing hypotheses. In this case, the Bayes factors can be severely biased whereas the modified ROPE approach gives a reasonable result. Finally, the connection leads to a simple and effective algorithm for computing Bayes factors using draws from posterior distributions generated by standard Bayesian programs such as BUGS, JAGS, and Stan.
AB - There has been strong recent interest in testing interval null hypotheses for improved scientific inference. For example, Lakens et al. and Lakens and Harms use this approach to study if there is a prespecified meaningful treatment effect in gerontology and clinical trials, instead of a point null hypothesis of any effect. Two popular Bayesian approaches are available for interval null hypothesis testing. One is the standard Bayes factor and the other is the region of practical equivalence (ROPE) procedure championed by Kruschke and others over many years. This article connects key quantities in the two approaches, which in turn allow us to contrast two major differences between the approaches with substantial practical implications. The first is that the Bayes factor depends heavily on the prior specification while a modified ROPE procedure is very robust. The second difference is concerned with the statistical property when data are generated under a neutral parameter value on the common boundary of competing hypotheses. In this case, the Bayes factors can be severely biased whereas the modified ROPE approach gives a reasonable result. Finally, the connection leads to a simple and effective algorithm for computing Bayes factors using draws from posterior distributions generated by standard Bayesian programs such as BUGS, JAGS, and Stan.
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U2 - 10.1080/00031305.2019.1701550
DO - 10.1080/00031305.2019.1701550
M3 - Article
AN - SCOPUS:85078072791
SN - 0003-1305
VL - 75
SP - 256
EP - 264
JO - American Statistician
JF - American Statistician
IS - 3
ER -