Optimal evidence accumulation in decision-making

(Medical Xpress)—At the same settings and light conditions, a camera will take the same picture every time. In contrast, a brain does not make perfect reconstructions of a stimulus. It appears instead to accumulate evidence ...


A brain mechanism that automatically links objects in our minds

When people see a toothbrush, a car, a tree—any individual object—their brain automatically associates it with other things it naturally occurs with, allowing humans to build context for their surroundings and set expectations ...

Oncology & Cancer

Advancing the study of T cells to improve immunotherapy

UT Southwestern scientists have developed a new method to study the molecular characteristics of T cells, critical immune cells that recognize and attack invaders in the body such as viruses, bacteria, and cancer.

Diseases, Conditions, Syndromes

Understanding the spread of infectious diseases

Scientists worldwide have been working feverishly on research into infectious diseases in the wake of the global outbreak of the COVID-19 disease, caused by the new coronavirus SARS-CoV-2. This concerns not only virologists, ...

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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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