Bayes factors work with comparing models. There is no null model. What, 0% effect? Ok, there was a non-zero effect. That model loses since it put the probability of 0% at 1 and everything else at 0. And if you do anything else, you’re encoding some amount of belief into the model, some judgment you’ve made.
So, you need to pick two models and compare them. I’m not saying this is right for science. It’s working well for my purposes. One model meaning “as planned”, one model meaning “not as planned”, use the Bayes factor to decide if things are going as planned. But you do need to be explicit about what models you’re comparing. You have to be able to just put some data in and get a probability back, or it’s not going to work.
It is the same way with traditional hypothesis testing. You take two models and compare their likehood.
It is the same way with traditional hypothesis testing. You take two models and compare their likehood.
With a Bayes factor you compare the marginal likelihood. You have to account for the weight of the parameters according to the priors. With a likelihood ratio, you pick the best parameters and take the ratio of those likelihoods.
This means a model used in a Bayes factor must be able to make predictions that follow probability axioms. Models in likelihood ratios don’t have this restriction.
I agree likelihood ratios and Bayes factors are similar. They’re also different.
With a Bayes factor you compare the marginal likelihood. You have to account for the weight of the parameters according to the priors. With a likelihood ratio, you pick the best parameters and take the ratio of those likelihoods.
Yeah, that's the difference that I mentioned. And seems very different from whatever "it put the probability of 0% at 1 and everything else at 0" is supposed to refer to.
This means a model used in a Bayes factor must be able to make predictions that follow probability axioms. Models in likelihood ratios don’t have this restriction.
Models in likehood ratios absolutely have to follow probability axioms, otherwise it would make no sense to apply probability axioms to study them.
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Then I don't get the meaning of this:
It is the same way with traditional hypothesis testing. You take two models and compare their likehood.
With a Bayes factor you compare the marginal likelihood. You have to account for the weight of the parameters according to the priors. With a likelihood ratio, you pick the best parameters and take the ratio of those likelihoods.
This means a model used in a Bayes factor must be able to make predictions that follow probability axioms. Models in likelihood ratios don’t have this restriction.
I agree likelihood ratios and Bayes factors are similar. They’re also different.
Yeah, that's the difference that I mentioned. And seems very different from whatever "it put the probability of 0% at 1 and everything else at 0" is supposed to refer to.
Models in likehood ratios absolutely have to follow probability axioms, otherwise it would make no sense to apply probability axioms to study them.