# What is Bayesian Evidence?

Could someone explain this concept or give a link to the explanation of this concept please? I know what "Bayesian" is, but I don't know what "Bayesian evidence" is. A good explanation of "evidence" will also be appreciated.

• Not sure exactly what is meant by "Bayesian Evidence." I don't really think this is a thing. A quick search suggested these topics might be related: en.wikipedia.org/wiki/Evidence_under_Bayes_theorem , en.wikipedia.org/wiki/Bayesian_inference (I could imagine someone mispronouncing 'inference' as 'evidence'.) – Newb Oct 29 '13 at 5:54
• @Newb Thanks for the reply. I think hejseb is right. This term shows up in a paper for several times and I'm sure that this is not a misspell. Maybe this is just an informal way to say it among non-mathematicians (I'm not sure). – xuhdev Oct 30 '13 at 22:16

This is a concept used in Bayesian model selection. Essentially, it's the probability of the data in some model $\mathcal{M}$ when the parameter uncertainty has been integrated out. Mathematically, it is
$$Pr(D|\mathcal{M})=\int_{\Theta}Pr(D|\theta)Pr(\theta|\mathcal{M})d\theta$$ where $\Theta$ is the domain of $\theta$. Using the evidence of different models you can compute the Bayes factor, for example.