Any example where there are more than two potential hypotheses.
Note, that for example, “this coin is unbiased”, “this coin is biased toward heads with p=.61″, and “this coin is biased toward heads with p=.62” count as three different hypotheses for this purpose.
This is fair as a criticism of log-odds, but in the example you give, one could avoid the issue of people having varying priors by just reporting the value of the likelihood function. However, this likelihood function reporting idea fails to be a practical summary in the context of massive models with lots of nuisance parameters.
Any example where there are more than two potential hypotheses.
Note, that for example, “this coin is unbiased”, “this coin is biased toward heads with p=.61″, and “this coin is biased toward heads with p=.62” count as three different hypotheses for this purpose.
This is fair as a criticism of log-odds, but in the example you give, one could avoid the issue of people having varying priors by just reporting the value of the likelihood function. However, this likelihood function reporting idea fails to be a practical summary in the context of massive models with lots of nuisance parameters.