Computer Sciences

A better statistical model for environmental data

By clarifying inconsistencies in published theories and devising a flexible statistical model, KAUST researchers have established a more informed and reliable basis for selecting the most suitable statistical model for environmental ...

Computer Sciences

Predicting British railway delays using artificial intelligence

Over the past 20 years, the number of passengers traveling on British train networks has almost doubled to 1.7 billion annually. With numbers like that it's clear how much people rely on rail service in Great Britain, and ...

Energy & Green Tech

Wind forecasts power up for reliable energy production

Optimizing the integration of wind energy into a country's power network requires reliable forecasts of how wind speed and direction are likely to vary in time and space over the pending few hours. KAUST researchers have ...

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Statistical model

A statistical model is a set of mathematical equations which describe the behavior of an object of study in terms of random variables and their associated probability distributions. If the model has only one equation it is called a single-equation model, whereas if it has more than one equation, it is known as a multiple-equation model.

In mathematical terms, a statistical model is frequently thought of as a pair (Y,P) where Y is the set of possible observations and P the set of possible probability distributions on Y. It is assumed that there is a distinct element of P which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are likely to be the true one.

Three notions are sufficient to describe all statistical models.

One of the most basic models is the simple linear regression model which assumes a relationship between two random variables Y and X. For instance, one may want to linearly explain child mortality in a given country by its GDP. This is a statistical model because the relationship need not to be perfect and the model includes a disturbance term which accounts for other effects on child mortality other than GDP.

As a second example, Bayes theorem in its raw form may be intractable, but assuming a general model H allows it to become

which may be easier. Models can also be compared using measures such as Bayes factors or mean square error.

This text uses material from Wikipedia, licensed under CC BY-SA