# Mathematical Metamodel

A Mathematical Metamodel is a metamodel based on mathematical equations (a mathematical program).

**Context:**- It must have one or more Model Variables.
- It must have one or more grounded Model Parameters.
- It can range from being a Parametric Mathematical Model to being a Nonparametric Mathematical Model.
- It can, like any model, range from being a Descriptive Model to being a Predictive Model.
- ...

**Example(s):**- a Mathematical Functions Family.
- a Statistical Metamodel.
- a Linear Equation Model, that can represent a set of Linear Functions.
- a Logistic Model, that can represent a set of Logistic Functions.
- a Polynomial Model.
- a State-Space Model.
- …

**Counter-Example(s):****See:**Mathematical Modeling, Statistical Model.

## References

### 2014

- http://en.wikipedia.org/wiki/Mathematical_model
- A
**mathematical model**is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models, as far as logic is taken as a part of mathematics. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.

- A

### 1974

- (Baird, 1974) ⇒ Yonathan Bard. (1974). “Nonlinear Parameter Estimation." Academic Press. ISBN:0120782502
- QUOTE: We refer to the relations which supposedly describe a certain physical situation, as a
*model*. Typically, a model consists of one or more equations. The quantities appearing in the equations we classify into*variables*and*parameters*. The distinction between these is not always clear cut, and it frequently depends on the context in which the variables appear. Usually a model is designed to explain the relationships that exist among quantities which can be measured independently in an experiment; these are the variables of the model. To formulate these relationships, however, one frequently introduces “constants" which stand for inherent properties of nature (or of the materials and equipment used in a given experiment). These are the parameters.

- QUOTE: We refer to the relations which supposedly describe a certain physical situation, as a