Data scientists build more honest prediction models

On Nov. 3, 2020—and for many days after—millions of people kept a wary eye on the presidential election prediction models run by various news outlets. With such high stakes in play, every tick of a tally and twitch of ...

Comet from edge of solar system killed the dinosaurs: study

Sixty-six million years ago, a huge celestial object struck off the coast of what is now Mexico, triggering a catastrophic "impact winter" that eventually wiped out three-quarters of life on Earth, including the dinosaurs.

Geoscientists reconstruct 6.5 million years of sea level stands

The pressing concern posed by rising sea levels has created a critical need for scientists to precisely predict how quickly the oceans will rise in coming centuries. To gain insight into future ice sheet stability and sea-level ...

Motherhood does not drive support for gun control

Moms are not more likely than other women to support gun control efforts. In fact, a new study finds that parenthood doesn't have a substantial effect on the gun control views of men or women.

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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