= Marginal likelihood from a nuisance-free statistic
= Marginal statistical likelihood
{synonym}
If a statistic T has marginal density depending on a parameter of interest but not on a nuisance parameter, that density gives a likelihood for the interest parameter. It is obtained by integrating out other observed coordinates. In contrast, <profile likelihood> maximizes the full likelihood over the nuisance parameter. This sampling-statistic construction is different from Bayesian model evidence, which integrates parameters against a prior. No prior is required for a nuisance-free sampling marginal.
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