## ::Statistical model

### ::concepts

Model::models Mathcal::theta First::''b'' Gaussian::theta Example::''i'' Harvnb::which

A **statistical model** embodies a set of assumptions concerning the generation of the observed data, and similar data from a larger population. A model represents, often in considerably idealized form, the data-generating process. The model assumptions describe a set of probability distributions, some of which are assumed to adequately approximate the distribution from which a particular data set is sampled.

A model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, "a model is a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).<ref>{{#invoke:Footnotes|harvard_citation_no_bracket}}</ref>

All statistical hypothesis tests and all statistical estimators are derived from statistical models. More generally, statistical models are part of the foundation of statistical inference.

**Statistical model sections**

Intro Formal definition An example General remarks Dimension of a model Nested models Comparing models See also Notes References Further reading

PREVIOUS: Intro | NEXT: Formal definition |

<< | >> |