I am trying to find the Bayes factor between two models, which I understand is the ratio of the likelihood functions of each model.

The second model has a uniform prior described by:

$U(A; -a, a) = \frac{\theta(A - -a)\theta(a - A)}{2a}$, where $\theta$ represents the Heaviside step function.

I also have a sampling distribution that takes the form P$(d|m,\omega)$, where $d$ is the data and $m$ is the mean. However, as the second model I refer to is not fully-encapsulated by this sampling distribution (hence the introduction of the prior), I am unsure if I can use this to determine the posterior/likelihood.

Does anyone have any tips for how I can go about determining the likelihood for this model?

Thank you!

Edited for clarity

  • $\begingroup$ I worry that you misread the other question. Even in the title of the question you link to, the prior is not equal to the likelihood. The posterior is equal to the likelihood. $\endgroup$ – Arya McCarthy Mar 16 at 18:12
  • $\begingroup$ If you don’t know the form of your likelihood, that’s a separate problem. You choose your likelihood function by specifying your model. $\endgroup$ – Arya McCarthy Mar 16 at 18:14
  • $\begingroup$ Apologies, I did misread the linked question. I have edited my original question to make things clearer. This is the only information I have on the model, so I am very unsure if I can determine the posterior or likelihood from this. $\endgroup$ – ConstantlyConfused Mar 16 at 20:31
  • $\begingroup$ Please use $\LaTeX$ markup in yor question. A guide is here: math.meta.stackexchange.com/questions/5020/… $\endgroup$ – kjetil b halvorsen Mar 17 at 0:27
  • $\begingroup$ “The second model I refer to is not fully-encapsulated by this sampling distribution”—what do you mean here? Why isn’t this the same as your likelihood function? $\endgroup$ – Arya McCarthy Mar 17 at 21:05

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