Research led by physicists and geographers at the University of Cambridge has unveiled some large-scale changes in the vegetation in the South American Andes which may have dramatic impact on the environment and ecosystems ...
Earth Sciences
Jul 21, 2023
4
369
Neural networks have been powering breakthroughs in artificial intelligence, including the large language models that are now being used in a wide range of applications, from finance, to human resources to health care. But ...
Mathematics
Mar 12, 2024
0
231
Even though the black hole at the center of the Milky Way is a monster, it's still rather quiet. Called Sagittarius A*, it's about 4.6 million times more massive than the sun. Usually, it's a brooding behemoth. But scientists ...
Astronomy
Aug 14, 2019
96
7879
The field of evolutionary biology has seen its share of spirited debates. But if there's one principle that virtually every expert in the field agrees on, it's that natural selection occurs at the level of the genome.
Evolution
Jan 16, 2020
9
1870
Most schoolchildren learn that the Earth has three (or four) layers: a crust, mantle and core, which is sometimes subdivided into an inner and outer core. That's not wrong, but it does leave out several other layers that ...
Earth Sciences
Feb 14, 2019
14
1261
Take events from the past, build a statistical model, and tell the future. Why not apply the formula to novels? Can contents in future books be predicted based only on data from existing ones? Richard Vale at the University ...
Researchers at Tel Aviv University have found changes in the morphology of many birds in Israel over the past 70 years, which they interpret to be a response to climate change. The body mass of some species decreased, while ...
Evolution
Apr 5, 2022
0
83
How many matter particles exist in nature? Particle physicists have been dealing with this question for a long time. The 12 matter particles contained in the standard model of particle physics? Or are there further particles ...
General Physics
Dec 13, 2012
54
5
A new data-driven statistical model that incorporates the surrounding landscape in unprecedented detail describes the transfer of an inserted bacterial gene via pollen and seed dispersal in cotton plants more accurately than ...
Biotechnology
Nov 30, 2010
0
0
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 ...
Mathematics
Mar 19, 2021
2
8
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
