Abstract
It is quite common for one data variable to depend statistically upon another variable. This is similar to the input-output relationship of a function such as \( y = \sin {}(x) \) except that the relationship between x and y is statistical rather than exact. Because of this similarity we call a model of such a relationship a function-model with an input datum id and an output datum od. od is also called the dependent variable and id the independent variable. A datum is now bivariate, d = 〈id, od〉, but note that id and od can themselves be multivariate. For example, if od is conditional on id 1 and on id 2 we can say that it is dependent on the pair 〈id 1, id 2〉. Just as we talk of data from a data-space, we also have input-data from an input-(data-)space and output-data from an output-(data-)space.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The packaging of a parameterised M and an estimator Est inside an unparameterised UPFunctionModel is simply often convenient and, as for UPModel.M and UPModel.Est in UPModel (Sect. 1.3), is not compulsory.
References
H.B. Curry, R. Feys, Combinatory Logic (North Holland, Amsterdam, 1958)
F. Galton, Section H. Anthropology. Opening address by Francis Galton. Nature 82, 507–510 (1885). https://doi.org/10.1038/032502a0. David (First (?) occurrence of common terms in mathematical statistics. Am. Stat. 49(2), 121–133 (1995). https://doi.org/10.2307/2684625. http://www.jstor.org/stable/2684625) attributes the “first (?)” occurrence of the term “regression” to this address
F. Galton, Kinship and correlation. Stat. Sci. 4(2), 81–86 (1989, reprinted). https://doi.org/10.1214/ss/1177012581. http://www.jstor.org/stable/2245330
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Allison, L. (2018). Function-Models. In: Coding Ockham's Razor. Springer, Cham. https://doi.org/10.1007/978-3-319-76433-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-76433-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76432-0
Online ISBN: 978-3-319-76433-7
eBook Packages: Computer ScienceComputer Science (R0)