All models are wrong; some models are useful Essay

All models are wrong; some models are useful - Essay Example Mathematical models are therefore very useful because Mathematics itself is an abstract language; enables us to make the representation numerically and visually, and offers powerful tools and techniques for quantitative analysis and forecasting. Usually, this involves defining constants, assigning variables, and forming structures such as functions, equations, diagrams, graphs etc. that establish the relationships between the various quantities. For example, car journeys, traffic patterns, and airline routes can all be modeled using matrices. However, despite the aforementioned features of mathematical modeling, it has limitations too. The most fundamental perhaps is the trade-off between simplicity and accuracy of the model. Usually, more complex models tend to improve its accuracy but at the same time of course make it more complicated to handle, which could also mean greater cost and required time. Therefore, when deciding which model to choose, the level of accuracy required balanced against need and the available resources is the most important consideration. If more than one different model is able to forecast with equal predictive accuracy, the Occam’s Razor principle suggests choosing the simplest model. With regards to forecasting, mathematical models can often be tested for accuracy using empirical or experimental data. If it is able to describe this accurately, it can then be used for forecasting purposes, for which several methods exist. These include moving averages, exponential smoothing, techniques for extrapolating time series with tend and seasonal components, and regression models. In all of these however, there are gaps between the complexity of the real world and the simplicity of these abstract models. The model’s true usefulness would then be tested if the extrapolation to other or future data or situations proves successful. Time series and forecasting is one of