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Marginal Likelihood (p₍X₎) ○◂｜Definition｜1st｜20261022184457-00-⌔
Marginal likelihood - Wikipedia
Marginal likelihood
A marginal likelihood is a likelihood function that has been integrated over the parameter space. In Bayesian statistics, it represents the probability of generating the observed sample for all possible values of the parameters; it can be understood as the probability of the model itself and is therefore often referred to as model evidence or simply evidence.
Due to the integration over the parameter space, the marginal likelihood does not directly depend upon the parameters. If the focus is not on model comparison, the marginal likelihood is simply the normalizing constant that ensures that the posterior is a proper probability. It is related to the partition function in statistical mechanics.1
Printed 2026-10-22.
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Link to original Footnotes
Šmídl, Václav; Quinn, Anthony (2006). “Bayesian Theory”. The Variational Bayes Method in Signal Processing. Springer. pp. 13–23. doi:10.1007/3-540-28820-1_2. ↩