Understanding the 'fundamental nature' of atomic-scale defects

Materials scientists study metals, polymers, and other substances at the atomic level in order to find new ways to control a material's physical properties, such as how strong or how malleable it is. One key aspect of this ...

Can we estimate the time until the next recession?

As the world economy is falling into one of the biggest contractions of the last decades, a new study of economic recession patterns finds that the likelihood of a downturn was high even before the onset of the Coronavirus ...

Plant disease primarily spreads via roadsides

An analysis based on mathematical statistics more precise than those previously carried out uncovered the reason why powdery mildew fungi on Åland are most abundant in roadsides and crossings. The specific cause was the ...

New LHCb analysis still sees previous intriguing results

At a seminar today at CERN, the LHCb collaboration presented a new analysis of data from a specific transformation, or "decay," that a particle called B0 meson can undergo. The analysis is based on twice as many B0 decays ...

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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.

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