A Bayes factor is the ratio of the likelihood of one particular hypothesis to the likelihood of another. It can be interpreted as a measure of the strength of evidence in favor of one theory among two competing theories.
Bayes factor gives us a way to evaluate the data in favor of a null hypothesis,
If the BF01 is 5 then it means the null hypothesis is 5 times as likely as the alternative hypothesis given the data. Conversely, if the BF01 is 1/5 then it means that the alternative hypothesis is 5 times as likely as the null hypothesis given the data.
N.B: BF10 = 1/BF01.
BF10 indicates the Bayes factor in favor of H1 over H0, whereas BF01 indicates the Bayes factor in favor of H0 over H1.
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|
If loge(BF01) is |
then you have… |
|
≥ 2 |
Extreme evidence for H0 |
|
1.5- <2 |
Very strong evidence for H0 |
|
1- <1.5 |
Strong evidence for H0 |
|
.5- <1 |
Moderate evidence for H0 |
|
0 - <.5 |
Anecdotal/weak evidence for H0 |
|
|
No evidence |
|
Negative |
Anecdotal evidence for H1 |
|
Moderate evidence for H1 |
|
|
Strong evidence for H1 |
|
|
Very strong evidence for H1 |
|
|
Extreme evidence for H1 |
loge (BF01) = -0.18 means that there is more evidence for the alternative hypothesis but it's anecdotal/weak.
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The default Cauchy is centered on 0 and has a scale factor "r" that determines the width.
This scale factor happens to equal the
interquartile range, such that, when r=0.707 for instance, 50% of the
prior mass lies in the interval from -0.707 to +0.707.
N.B. Any comments, explanations, additions or corrections are welcome
Update: I found a great video explaining similar results at yuzaR Data Science channel; from which I found this great explanation:
Resources:
https://ptfonseca.github.io/pcal/reference/bfactor_log_interpret.html
https://www.statology.org/bayes-factor/
https://www.statisticshowto.com/bayes-factor-definition/
https://forum.cogsci.nl/discussion/3236/setting-cauchy-prior-scaling-in-bayesian-t-test-use-related-effect-size
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