Statistical models are used in applied statistics. Three notions are sufficient to describe all statistical models.

1. We choose a statistical unit, such as a person, to observe directly. Multiple observations of the same unit over time is called longitudinal research. Observations of multiple statistical attributes is a common way of studying relationships among the attributes of a single unit.
2. Our interest may be in a statistical population (or set) of similar units rather than in any individual unit. Survey sampling offers an example of this type of modeling.
3. Our interest may focus on a statistical assembly where we examine functional subunits of the statistical unit. For example, Physiology modeling probes the organs which compose the unit. A common model for this type of research is the stimulus-response model.

In mathematical terms, a statistical model is frequently thought of as a parameterized set of probability distributions of the form

\{ P_\theta | \theta \in \Theta \}.

It is assumed that there is a distinct element in the above set which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are likely to be the true one.

So, for example, Bayes theorem in its raw form may be intractable, but assuming a general model H allows it to become

P(A | B,H) = \frac{P(B | A,H) P(A | H)}{P(B | H)}

which may be easier. Models can also be compared using measures such as Bayes factors or mean square error.

See also

• A/B testing
• Statistical model validation

es:Modelo estadístico fr:Modčle statistique pl:Model statystyczny