Editing Marginal likelihood (section)

{{Short description|In Bayesian probability theory}}
{{Bayesian statistics}}
A '''marginal likelihood''' is a [[likelihood function]] that has been [[Integral|integrated]] over the [[parameter space]]. In [[Bayesian statistics]], it represents the probability of generating the [[Sampling (statistics)|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 probability|posterior]] is a proper probability. It is related to the [[Partition function (statistical mechanics)|partition function in statistical mechanics]].<ref>{{cite book |first=Václav |last=Šmídl |first2=Anthony |last2=Quinn |chapter=Bayesian Theory |title=The Variational Bayes Method in Signal Processing |pages=13–23 |year=2006 |publisher=Springer |doi=10.1007/3-540-28820-1_2 }}</ref>