Applied probability
Encyclopedia
Much research involving probability
is done under the auspices of applied probability, the application of probability theory
to other scientific and engineering
domains. However, while such research is motivated (to some degree) by applied problems, it is usually the mathematical
aspects of the problems that are of most interest to researchers (as is typical of applied mathematics
in general).
Applied probabilists are particularly concerned with the application of stochastic process
es, and probability more generally, to the natural, applied and social sciences, including biology
, physics
(including astronomy
), chemistry
, computer science
and information technology
, and economics
.
Another area of interest is in engineering
, particularly in areas of uncertainty
, or risks.
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
is done under the auspices of applied probability, the application of probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
to other scientific and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
domains. However, while such research is motivated (to some degree) by applied problems, it is usually the mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
aspects of the problems that are of most interest to researchers (as is typical of applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
in general).
Applied probabilists are particularly concerned with the application of stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es, and probability more generally, to the natural, applied and social sciences, including biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
(including astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
), chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
and information technology
Information technology
Information technology is the acquisition, processing, storage and dissemination of vocal, pictorial, textual and numerical information by a microelectronics-based combination of computing and telecommunications...
, and economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
.
Another area of interest is in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, particularly in areas of uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
, or risks.
See also
- Areas of application:
- Ruin theoryRuin theoryRuin theory, sometimes referred to as collective risk theory, is a branch of actuarial science that studies an insurer's vulnerability to insolvency based on mathematical modeling of the insurer's surplus....
- Statistical physicsStatistical physicsStatistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...
- StoichiometryStoichiometryStoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers...
and modelling chemical reactionChemical reactionA chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
s - EcologyEcologyEcology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
, particularly population modelling - Evolutionary biologyEvolutionEvolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
- OptimizationOptimization (computer science)In computer science, program optimization or software optimization is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources...
in computer scienceComputer scienceComputer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems... - TelecommunicationTelecommunicationTelecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
s - Options pricing in economicsEconomicsEconomics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
- Ewens's sampling formulaEwens's sampling formulaIn population genetics, Ewens' sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample.-Definition:...
in population geneticsPopulation geneticsPopulation genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population... - Operations researchOperations researchOperations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
- Gaming mathematicsGaming mathematicsGaming mathematics, also referred to as the mathematics of gambling, is a collection of probability applications encountered in games of chance and can be included in applied mathematics...
- Ruin theory
- Stochastic processStochastic processIn probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es:- Markov chainMarkov chainA Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
- Poisson processPoisson processA Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
- Brownian motionBrownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
and other diffusion processes. - Queueing theoryQueueing theoryQueueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
- Renewal theoryRenewal theoryRenewal theory is the branch of probability theory that generalizes Poisson processes for arbitrary holding times. Applications include calculating the expected time for a monkey who is randomly tapping at a keyboard to type the word Macbeth and comparing the long-term benefits of different...
- Markov chain
- Additional information and resources
- INFORMS Institute for Operations Research and the Management Sciences
Further reading
- Baeza-Yates, R. (2005) Recent advances in applied probability, Springer. ISBN 0387233784
- Blake, I.F. (1981) Introduction to Applied Probability, Wiley. ISBN 0471060828