12 Facts About Mathematical model

Mathematical model is a description of a system using mathematical concepts and language.

For example, if we make a Mathematical model of how a medicine works in a human system, we know that usually the amount of medicine in the blood is an exponentially decaying function.

Alternatively, the NARMAX algorithms which were developed as part of nonlinear system identification can be used to select the Mathematical model terms, determine the Mathematical model structure, and estimate the unknown parameters in the presence of correlated and nonlinear noise.

In general, Mathematical model complexity involves a trade-off between simplicity and accuracy of the Mathematical model.

Still, Newton's Mathematical model is quite sufficient for most ordinary-life situations, that is, as long as particle speeds are well below the speed of light, and we study macro-particles only.

Any Mathematical model which is not pure white-box contains some parameters that can be used to fit the Mathematical model to the system it is intended to describe.

Usually, the easiest part of Mathematical model evaluation is checking whether a Mathematical model fits experimental measurements or other empirical data.

Tools from nonparametric statistics can sometimes be used to evaluate how well the data fit a known distribution or to come up with a general model that makes only minimal assumptions about the model's mathematical form.

Question of whether the Mathematical model describes well the properties of the system between data points is called interpolation, and the same question for events or data points outside the observed data is called extrapolation.

One can argue that a Mathematical model is worthless unless it provides some insight which goes beyond what is already known from direct investigation of the phenomenon being studied.

Mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables.

The actual Mathematical model is the set of functions that describe the relations between the different variables.