In Bayes theorem of a parameter $theta$ with data $D$, we have:

$$P(theta|D) = frac{P(D|theta)P(theta)}{P(D)}$$

where I know $P(D)$ as the marginal likelihood. Is it true that the marginal likelihood is referred to as evidence in Bayesian statistics? If not what is commonly refered to as evidence?

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#### Best Answer

$P(D)$ is the *model evidence*, unfortunately "model" is often dropped. The model evidence is also referred to as *marginal likelihood*.

Wikipedia calls the data $D$ the *evidence*.

The *model evidence* is defined as:

$int,P(theta|D)dtheta$

It is called the *model* evidence, since the larger its value, the more apt the model is generally fitting the data.

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