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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