List of fields of application of statistics

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Statistics is the mathematical science involving the collection, analysis and interpretation of data. A number of specialties have evolved to apply statistical and methods to various disciplines. Certain topics have "statistical" in their name but relate to manipulations of probability distributions rather than to statistical analysis.

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A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences and engineering disciplines, as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right.

<span class="mw-page-title-main">Probability</span> Branch of mathematics concerning chance and uncertainty

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability. The probability of an impossible event is 0; that of an event that is certain to occur is 1. The probabilities of two complementary events A and B – either A occurs or B occurs – add up to 1. A simple example is the tossing of a fair (unbiased) coin. If a coin is fair, the two possible outcomes are equally likely; since these two outcomes are complementary and the probability of "heads" equals the probability of "tails", the probability of each of the two outcomes equals 1/2.

The following outline is provided as an overview of and topical guide to physics:

<span class="mw-page-title-main">Statistics</span> Study of the collection, analysis, interpretation, and presentation of data

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.

Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.

Stochastic refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a stochastic process is also referred to as a random process.

<span class="mw-page-title-main">Mathematical statistics</span> Branch of statistics

Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.

Computational science, also known as scientific computing, technical computing or scientific computation (SC), is an area of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes

<span class="mw-page-title-main">Mathematical psychology</span> Mathematical modeling of psychological theories and phenomena

Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations. There are five major research areas in mathematical psychology: learning and memory, perception and psychophysics, choice and decision-making, language and thinking, and measurement and scaling.

<span class="mw-page-title-main">Branches of science</span> Overview of the disciplines of study

The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups:

The foundations of statistics concern the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's "significance testing" and Neyman–Pearson "hypothesis testing", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution.

<span class="mw-page-title-main">Branches of physics</span> Overview of the branches of physics

Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.

<span class="mw-page-title-main">Applied mathematics</span> Application of mathematical methods to other fields

Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

The social sciences are the sciences concerned with societies, human behaviour, and social relationships.

The following outline is provided as an overview of and topical guide to formal science:

The following outline is provided as an overview of and topical guide to applied science:

Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.

The CEREMADE is a research centre in Mathematics within Université Paris-Dauphine. It was created in 1970.