that doesn’t seem very useful and I’ve never seen anyone do that.
Yes. That’s why it’s a straw man. I’m being sort of uncharitable in that description. My point is that’s a starting point. To go from there, you need to choose a model which will have parameters or priors.
That’s where the « null hypothesis » comes in. If it fixes the parameters in the model you get a well-defined « null » model with a well-defined probability distribution for the observation and - just like you can take this null hypothesis model and do frequentist calculations with it - you can take this model and calculate a Bayes factor relative to some other model.
(To be clear, if the null hypothesis doesn’t fully specify the parameters the preceding paragraph doesnt apply and the situation is more complex.)
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Yes. That’s why it’s a straw man. I’m being sort of uncharitable in that description. My point is that’s a starting point. To go from there, you need to choose a model which will have parameters or priors.
That’s where the « null hypothesis » comes in. If it fixes the parameters in the model you get a well-defined « null » model with a well-defined probability distribution for the observation and - just like you can take this null hypothesis model and do frequentist calculations with it - you can take this model and calculate a Bayes factor relative to some other model.
(To be clear, if the null hypothesis doesn’t fully specify the parameters the preceding paragraph doesnt apply and the situation is more complex.)