Search results
Results from the WOW.Com Content Network
Modeling and simulation are important in research. Representing the real systems either via physical reproductions at smaller scale, or via mathematical models that allow representing the dynamics of the system via simulation, allows exploring system behavior in an articulated way which is often either not possible, or too risky in the real world.
The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social ...
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict.
By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area.
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process . [ 1 ]
Figure 1. Schematic representation of uncertainty analysis and sensitivity analysis. In mathematical modeling, uncertainty arises from a variety of sources - errors in input data, parameter estimation and approximation procedure, underlying hypothesis, choice of model, alternative model structures and so on.
In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". [1] An overfitted model is a mathematical model that contains more parameters than can be justified by the data. [2]
This illustrates the pitfalls of relying solely on a fitted model to understand the relationship between variables. A fitted linear regression model can be used to identify the relationship between a single predictor variable x j and the response variable y when all the other