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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.

**Actuarial science**is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries.**Astrostatistics**is the discipline that applies statistical analysis to the understanding of astronomical data.**Biostatistics**is a branch of biology that studies biological phenomena and observations by means of statistical analysis, and includes medical statistics.**Business analytics**is a rapidly developing business process that applies statistical methods to data sets (often very large) to develop new insights and understanding of business performance & opportunities**Chemometrics**is the science of relating measurements made on a chemical system or process to the state of the system via application of mathematical or statistical methods.**Demography**is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space.**Econometrics**is a branch of economics that applies statistical methods to the empirical study of economic theories and relationships.**Environmental statistics**is the application of statistical methods to environmental science. Weather, climate, air and water quality are included, as are studies of plant and animal populations.**Epidemiology**is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.**Forensic statistics**is the application of probability models and statistical techniques to scientific evidence, such as DNA evidence, and the law. In contrast to "everyday" statistics, to not engender bias or unduly draw conclusions, forensic statisticians report likelihoods as likelihood ratios (LR).**Geostatistics**is a branch of geography that deals with the analysis of data from disciplines such as petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geography.**Jurimetrics**is the application of probability and statistics to law.**Machine learning**is the subfield of computer science that formulates algorithms in order to make predictions from data.**Operations research**(or operational research) is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems.**Population ecology**is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment.**Psychometrics**is the theory and technique of educational and psychological measurement of knowledge, abilities, attitudes, and personality traits.**Quality control**reviews the factors involved in manufacturing and production; it can make use of statistical sampling of product items to aid decisions in process control or in accepting deliveries.**Quantitative psychology**is the science of statistically explaining and changing mental processes and behaviors in humans.**Reliability engineering**is the study of the ability of a system or component to perform its required functions under stated conditions for a specified period of time**Statistical finance**, an area of econophysics, is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets.**Statistical mechanics**is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.**Statistical physics**is one of the fundamental theories of physics, and uses methods of probability theory in solving physical problems.**Statistical signal processing**utilizes the statistical properties of signals to perform signal processing tasks.**Statistical thermodynamics**is the study of the microscopic behaviors of thermodynamic systems using probability theory and provides a molecular level interpretation of thermodynamic quantities such as work, heat, free energy, and entropy.

**Management science** (**MS**) is the broad interdisciplinary study of problem solving and decision making in human organizations, with strong links to **management**, economics, business, engineering, management consulting, and other fields. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and accurate management decisions by arriving at optimal or near optimal solutions to complex decision problems. Management science helps businesses to achieve goals using various scientific methods.

**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. See glossary of probability and statistics.

**Statistical inference** is the process of using data analysis to deduce properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.

**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.

**Theoretical chemistry** is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, molecule activation, etc.

**Monte Carlo methods**, or **Monte Carlo experiments**, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

**Computational archaeology** describes computer-based analytical methods for the study of long-term human behaviour and behavioural evolution. As with other sub-disciplines that have prefixed 'computational' to their name, the term is reserved for methods that could not realistically be performed without the aid of a computer.

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

**Stochastic** refers to a randomly determined process. The word first appeared in English to describe a mathematical object called a stochastic process, but now in mathematics the terms *stochastic process* and *random process* are considered interchangeable. The word, with its current definition meaning random, came from German, but it originally came from Greek στόχος* (stókhos)*, meaning 'aim, guess'.

**Theoretical computer science** (**TCS**) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

In natural and social sciences, and maybe in other fields, **quantitative research** is the systematic empirical investigation of observable phenomena via statistical, mathematical, or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observation and mathematical expression of quantitative relationships.

**Lists of mathematics topics** cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, integrals and reference tables. They also cover equations named after people, societies, mathematicians, journals and meta-lists.

**Computational science**, also known as **scientific computing** or **scientific computation** (**SC**), is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core it involves the development of models and simulations to understand natural systems.

**Ole Eiler Barndorff-Nielsen** is a Danish statistician who has contributed to many areas of statistical science.

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.

**Applied mathematics** is the application of mathematical methods by different fields such as science, engineering, 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 following outline is provided as an overview of and topical guide to formal science:

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

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