A novel tool to probe fundamental matter

Identifying elementary constituents of matter including quarks, bosons and electrons, and the manner by which these particles interact with each other, constitutes one of the greatest challenges in modern physical sciences. ...

A modeling tool to rapidly predict weed spread risk

In the study, published in the journal Methods in Ecology and Evolution, the researchers developed the tool that uses information about the features of a weed species and the geography of the area in which it has been reported ...

Finding (microbial) pillars of the bioenergy community

Stems, leaves, flowers and fruits make up the biggest chunk of potential living space for microbes in the environment, but ecologists still don't know a lot about how the microorganisms that reside there establish and maintain ...

Paris Agreement does not rule out ice-free Arctic

Research published in this week's issue of Nature Communications reveals a considerable chance for an ice-free Arctic Ocean at global warming limits stipulated in the Paris Agreement. Scientists from South Korea, Australia ...

See how humans have redrawn Earth's biological map

Humans are rapidly changing the distinctive biodiversity that evolved in regions of the Earth over millions of years by introducing new species and wiping out others, a new study has shown.

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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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