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 Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...

and finance industries. *

Astrostatistics Astrostatistics is a discipline which spans astrophysics, statistical analysis and data mining. It is used to process the vast amount of data produced by automated scanning of the cosmos, to characterize complex datasets, and to link astronomical d ...

is the discipline that applies statistical analysis to the understanding of astronomical data. * Biostatistics is a branch of

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

that studies biological phenomena and observations by means of statistical analysis, and includes

medical statistics Medical statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the Un ...

. *

Business analytics Business analytics (BA) refers to the skills, technologies, and practices for continuous iterative exploration and investigation of past business performance to gain insight and drive business planning. Business analytics focuses on developing ne ...

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 Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, a ...

is the science of relating measurements made on a

chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., w ...

system or process to the state of the system via application of mathematical or statistical methods. *

Demography Demography () is the statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as edu ...

is the statistical study of all

population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...

s. 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 Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...

is a branch of

economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...

that applies statistical methods to the empirical study of economic theories and relationships. *

Environmental statistics Environment statistics is the application of statistical methods to environmental science. It covers procedures for dealing with questions concerning the natural environment in its undisturbed state, the interaction of humanity with the environmen ...

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 Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evide ...

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 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 sta ...

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 Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including p ...

is a branch of

geography Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, an ...

that deals with the analysis of data from disciplines such as petroleum geology,

hydrogeology Hydrogeology (''hydro-'' meaning water, and ''-geology'' meaning the study of the Earth) is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust (commonly in aqui ...

hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is call ...

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

, oceanography,

geochemistry Geochemistry is the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth's crust and its oceans. The realm of geochemistry extends beyond the Earth, encompassing the ...

. *

Jurimetrics Jurimetrics is the application of quantitative methods, and often especially probability and statistics, to law. In the United States, the journal '' Jurimetrics'' is published by the American Bar Association and Arizona State University. The '' J ...

is the application of probability and statistics to

law Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. It has been vario ...

. *

Machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

is the subfield of

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...

that formulates algorithms in order to make predictions from data. *

Operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decis ...

(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;

Management science Management science (or managerial science) is a wide and interdisciplinary study of solving complex problems and making strategic decisions as it pertains to institutions, corporations, governments and other types of organizational entities. It is ...

focuses on problems in the business world. *

Population ecology Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment, such as birth and death rates, and by immigration and emigration. The discipline is import ...

is a sub-field of

ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overl ...

that deals with the dynamics of species populations and how these populations interact with the

environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...

. *

Psychometrics Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and ...

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 Quantitative psychology is a field of scientific study that focuses on the mathematical modeling, research design and methodology, and statistical analysis of psychological processes. It includes tests and other devices for measuring cognitive a ...

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 Econophysics is a heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynam ...

, is an empirical attempt to shift finance from its

normative Normative generally means relating to an evaluative standard. Normativity is the phenomenon in human societies of designating some actions or outcomes as good, desirable, or permissible, and others as bad, undesirable, or impermissible. A norm in ...

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 Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

, which includes mathematical tools for dealing with large populations, to the field of

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to object ...

, which is concerned with the motion of particles or objects when subjected to a force. *

Statistical physics Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approxim ...

is one of the fundamental theories of

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, and uses methods of probability theory in solving physical problems. *

Statistical signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...

utilizes the statistical properties of

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...

s to perform signal processing tasks. *

Statistical thermodynamics 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 b ...

is the study of the microscopic behaviors of

thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...

s using probability theory and provides a molecular level interpretation of thermodynamic quantities such as

work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal t ...

heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...

, free energy, and

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

See also