likelihoodu
Likelihoodu is a theoretical concept in statistics and probability, used primarily in educational and thought-experiment contexts to illustrate extensions of the likelihood principle. In this usage, likelihoodu refers to an extended likelihood function that also accounts for uncertainty in how data are collected, not just the observed outcomes. The core idea is to treat the likelihood as a function of model parameters after integrating over latent aspects of the data-generating process, such as measurement error, missing data, or sampling design.
In formal terms, likelihoodu builds on the standard likelihood, P(data | theta), by incorporating a data-collection mechanism
Applications include robustness to misspecification of the data process, handling of missing data, and evaluation of
History and usage: Likelihoodu is not an established term in mainstream statistics; it appears in some educational
See also: Likelihood, Maximum likelihood estimation, Latent-variable models, Measurement error, Data augmentation.