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0 pointskgwgk2y ago0 comments

> Choosing a null model for this purpose requires more assumptions than doing null hypothesis testing with frequentist statistics.

How so?

I could choose the same null model that predicts that the observation is distributed as, say, a standard Gaussian. What additional assumptions are required?

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travisjungroth2y ago· 2 in thread

Mean and standard deviation up front, not from the sample. At least, that would go against my understanding of Bayes factors and how I’ve calculated them. You can do other stats, t-test for example, without declaring that up front.

kgwgkOP2y ago

I don’t understand what you say, sorry.

If my choice of null model is p(x)=exp(-x^2/2) and I get some observation xobs I can do frequentist things with it - like calculating the p-value p(|x|>|xobs|) for example - and I can compare it with some alternative model p’(x) using the Bayes factor p(xobs)/p’(xobs).

What does “Mean and standard deviation up front, not from the sample.” mean in this context?

travisjungroth2y ago

Mean and standard deviation up front would mean that you set your null as a normal distribution with a mean of 0 and a standard deviation of 2%, for example. This is different from saying that you’ll just say it’s normal, and take the mean and standard deviation from the sample.

I mean, I could be wrong on this. You could do that if you want. I just think of Bayes factors as a competition and it needs to be “fair”. So it doesn’t make sense to let the null update as data comes in but not the alternative.

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