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Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Model in probability theory
In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal
Martingale (probability theory)
Martingale_(probability_theory)
Number measuring the chance an event occurs
computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe
Probability
When the occurrence of one event does not affect the likelihood of another
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically
Independence (probability theory)
Independence_(probability_theory)
Interpretation of probability
Bayesian probability (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is an interpretation of the concept of probability, in which, instead of frequency or
Bayesian_probability
In statistics and probability theory, set of outcomes to which a probability is assigned
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome
Event_(probability_theory)
Mathematical function for the probability a given outcome occurs in an experiment
In probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more
Probability_distribution
Model of information available at a given point of a random process
In the theory of stochastic processes, a subdiscipline of probability theory, filtrations are totally ordered collections of subsets that are used to
Filtration (probability theory)
Filtration_(probability_theory)
Fourier transform of the probability density function
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Interpretation of probability
Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability (the long-run probability) as the limit
Frequentist_probability
Foundations of probability theory
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. Like all axiomatic
Probability_axioms
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables
Stochastic_process
Philosophical interpretation of the axioms of probability
mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called
Probability_interpretations
Chances of card combinations in poker
ideas since long before the invention of poker. The development of probability theory in the late 1400s was attributed to gambling; when playing a game
Poker_probability
Mathematical framework to model epistemic uncertainty
as probability, possibility and imprecise probability theories. Introduced by Arthur P. Dempster in the context of statistical inference, the theory was
Dempster–Shafer_theory
Mathematical concept
In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct
Probability_space
Concept in probability theory
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It
Law_of_total_probability
Branch of applied probability theory
Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability to
Decision_theory
Probability distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes
Binomial_distribution
Concept in probability theory
of probability or classical interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace: The probability of
Classical definition of probability
Classical_definition_of_probability
Mathematical rule for inverting probabilities
In probability theory, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting
Bayes'_theorem
Procedure that can be infinitely repeated, with a well-defined set of outcomes
In probability theory, an experiment or trial (see below) is the mathematical model of any procedure that can be infinitely repeated and has a well-defined
Experiment (probability theory)
Experiment_(probability_theory)
Branch of probability theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While
Large_deviations_theory
Mathematical theory
on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given
Solomonoff's theory of inductive inference
Solomonoff's_theory_of_inductive_inference
Possible result of an experiment or trial
In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is a unique random element
Outcome_(probability)
Probability saying
In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the
Almost_surely
Diagram to represent a probability space in probability theory
In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such
Tree diagram (probability theory)
Tree_diagram_(probability_theory)
Inequalities in probability theory
In probability theory, Bernstein inequalities give bounds on the probability that the sum of random variables deviates from its mean. In the simplest
Bernstein inequalities (probability theory)
Bernstein_inequalities_(probability_theory)
Concept in probability theory
In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical
Total variation distance of probability measures
Total_variation_distance_of_probability_measures
Probability of an event occurring, given that another event has already occurred
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption
Conditional_probability
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence
Convergence of random variables
Convergence_of_random_variables
Description of continuous random distribution
In probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function
Probability_density_function
Observed value of a random variable
the corresponding lower case letters denote their realizations. In probability theory, a random variable is a function X {\displaystyle X} defined from
Realization_(probability)
Derivation of the laws of probability theory
laws of probability theory from a certain set of postulates. This derivation justifies the so-called "logical" interpretation of probability, as the laws
Cox's_theorem
Mathematical theory on behavior of connected clusters in a random graph
probability theory Bunkbed conjecture – Conjecture in probabilistic combinatorics Continuum percolation theory – Branch of mathematics in probability
Percolation_theory
In probability theory, two sequences of probability measures are said to be contiguous if asymptotically they share the same support. Thus the notion of
Contiguity (probability theory)
Contiguity_(probability_theory)
set by a collection of simpler subsets. In probability theory it is the approximation of one probability distribution by another. Let X be a set and
Ε-net (computational geometry)
Ε-net_(computational_geometry)
Generalization of the concept from statistical mechanics
partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition
Partition function (mathematics)
Partition_function_(mathematics)
Random process independent of past history
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability
Markov_chain
theorem (probability theory) Maxwell's theorem (probability theory) Optional stopping theorem (probability theory) Poisson limit theorem (probability) Raikov's
List_of_theorems
Academic journal
Probability Theory and Related Fields is a peer-reviewed mathematics journal published by Springer. Established in 1962, it was originally named Zeitschrift
Probability Theory and Related Fields
Probability_Theory_and_Related_Fields
Scientific study of digital information
needed] Much of the mathematics behind information theory with events of different probabilities were developed for the field of thermodynamics by Ludwig
Information_theory
Counterintuitive result in probability
classical probability suggests, aligning with Gregory Chaitin's modern theorem and building on algorithmic information theory and algorithmic probability by
Infinite_monkey_theorem
Mathematical theory on random variables
Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of
Free_probability
Theory of behavioral economics
money. The theory continues with a second concept, based on the observation that people attribute excessive weight to events with low probability and insufficient
Prospect_theory
Soviet mathematician (1903–1987)
mathematician who played a central role in the creation of modern probability theory. He also gave fundamental contributions to the mathematics of topology
Andrey_Kolmogorov
The order in probability notation is used in probability theory and statistical theory in direct parallel to the big O notation that is standard in mathematics
Big_O_in_probability_notation
term chance was also employed in the mathematical sense of "probability," with its theory often referred to as the "Doctrine of Chances." Chance comes
History_of_probability
Topics referred to by the same term
wedge product) Internal product, in a monoidal category Product (category theory), a generalization of mathematical products Fibre product or pullback Coproduct
Product
Randomly determined process
describes phenomena. These terms are often used interchangeably. In probability theory, the formal concept of a stochastic process is also referred to as
Stochastic
Mathematical theory for handling uncertainty
Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures
Possibility_theory
Concept in probability theory
In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes
Markov_kernel
Theorem from probability theory
In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) for the central limit
Lindeberg's_condition
Vector with non-negative entries that add up to one
statistics, a probability vector or stochastic vector is a vector with non-negative entries that add up to one. Underlying every probability vector is an
Probability_vector
lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Measure of total value one, generalizing probability distributions
(1995). Probability and Measure. John Wiley. ISBN 0-471-00710-2. Ash, Robert B.; Doléans-Dade, Catherine A. (1999). Probability & Measure Theory. Academic
Probability_measure
Discrete probability distribution
In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a
Poisson_distribution
Logarithm of probabilities, useful for calculations
In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing
Log_probability
Concept in combinatorial mathematics
importance because of (among other things) its application to the theory of free probability. The number of noncrossing partitions of a set of n elements is
Noncrossing_partition
Branch of mathematics that studies dynamical systems
properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated
Ergodic_theory
Probability theory for low quality data
Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague
Imprecise_probability
Written work by John Maynard Keynes
uncertainty than the more familiar and straightforward 'classical' theories of probability. This has since become known as a "logical-relationist" approach
A_Treatise_on_Probability
Average value of a random variable
In probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it
Expected_value
Soviet mathematician
partial differential equations, differential geometry, probability theory, and approximation theory. Bernstein was born into the Jewish family of prominent
Sergei_Bernstein
Probability theory paradox
Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités
Bertrand paradox (probability)
Bertrand_paradox_(probability)
Concept in probability theory
In probability theory and statistics, two real-valued random variables, X {\displaystyle X} , Y {\displaystyle Y} , are said to be uncorrelated if their
Uncorrelatedness
Chinese-American mathematician
Chinese-American mathematician known for his significant contributions to modern probability theory. Chung was a native of Hangzhou, the capital city of Zhejiang Province
Chung_Kai-lai
Probability theory concept
In probability theory, the chain rule (also called the general product rule) describes how to calculate the probability of the intersection of, not necessarily
Chain_rule_(probability)
Two propositions or events that cannot both be true
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example
Mutual_exclusivity
Type of probability distribution
} , that are defined on the same probability space, the joint probability distribution or multivariate probability distribution for X , Y , … {\displaystyle
Joint probability distribution
Joint_probability_distribution
American mathematician (1910–2004)
processes, developed martingale theory into a central method of probability, and pioneered probabilistic potential theory. His 1953 monograph Stochastic
Joseph_L._Doob
Paradox in decision theory
black balls within the single urn, and probability, of which red balls are drawn at 1/3 vs. 2/3. Utility theory models the choice by assuming that in
Ellsberg_paradox
Book by John von Neumann and Oskar Morgenstern
convenience. However, Neumann and Morgenstern mentioned that a theory of subjective probability could be provided, and this task was completed by Jimmie Savage
Theory of Games and Economic Behavior
Theory_of_Games_and_Economic_Behavior
Probability theory and statistics concept
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome
Conditional probability distribution
Conditional_probability_distribution
Power series derived from a discrete probability distribution
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of
Probability generating function
Probability_generating_function
Integral transform useful in probability theory, physics, and engineering
Marquis de Laplace, who used a similar transform in his work on probability theory. Laplace wrote extensively about the use of generating functions (1814)
Laplace_transform
Averages of repeated trials converge to the expected value
In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a large number of independent
Law_of_large_numbers
Probability estimate
In probability theory and statistics, the empirical probability or experimental probability of an event is an estimate of the probability of the event
Empirical_probability
Concept in probability theory
In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some
Markov's_inequality
Branch of discrete mathematics
problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas
Combinatorics
Stochastic process in probability theory
In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments:
Lévy_process
Proof technique in probability theory
In probability theory, coupling is a proof technique that allows one to compare two unrelated random variables (distributions) X and Y by creating a random
Coupling_(probability)
Function acting on function spaces
group, or the group of rotations. Operators are also involved in probability theory, such as expectation, variance, and covariance, which are used to
Operator_(mathematics)
Hypothesis in epistemological philosophy
probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain. That view holds profound
Radical_probabilism
Ratio of the probability of an event happening versus not happening
odds in Wiktionary, the free dictionary. In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used
Odds
catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals. For contributors
List_of_probability_topics
In probability theory, the method of moments is a way of proving convergence in distribution by proving convergence of a sequence of moment sequences.
Method of moments (probability theory)
Method_of_moments_(probability_theory)
Croatian–American mathematician
Srećko Feller, was a Croatian–American mathematician specializing in probability theory. Feller was born in Zagreb to Ida Oemichen-Perc, a Croatian–Austrian
William_Feller
Branch of mathematics
simplify many limit arguments. Measure theory also supplies the underlying mathematics of probability theory. A probability space is a measure space whose total
Mathematical_analysis
Base of natural logarithms
distinguished role in the theory of entropy in probability theory and ergodic theory. The basic idea is to consider a partition of a probability space into a finite
E_(mathematical_constant)
Matrix used to describe the transitions of a Markov chain
found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer
Stochastic_matrix
upper bound on the variance of any bounded probability distribution Bernstein inequalities (probability theory) Boole's inequality Borell–TIS inequality
List_of_inequalities
Probability distribution of the sum of random variables
convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds
Convolution of probability distributions
Convolution_of_probability_distributions
Probability that random variable X is less than or equal to x
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution
Cumulative distribution function
Cumulative_distribution_function
Russian mathematician (1931–2026)
Siberian school of probability theory founded by Kolmogorov and developed in Novosibirsk. His research spanned probability theory, mathematical statistics
Aleksandr_Borovkov
Italian mathematician
Fabio Toninelli (born 1975) is an Italian mathematician who works in probability theory, stochastic processes and probabilistic aspects of mathematical physics
Fabio_Toninelli
Probability distribution modeling a coin toss which need not be fair
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution
Bernoulli_distribution
Average uncertainty in variable's states
describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable X {\displaystyle
Entropy_(information_theory)
Philosophical problem-solving principle
increase the probability that the overall theory is wrong. There have also been other attempts to derive Occam's razor from probability theory, including
Occam's_razor
Application of quantum theory mathematics to cognitive phenomena
mathematical formalism of quantum probability theory to model psychology phenomena when classical probability theory fails. The field focuses on modeling
Quantum_cognition
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PROBABILITY THEORY
PROBABILITY THEORY
Surname or Lastname
English
English : in all probability an English variant of Scottish Lachlan (see McLachlan), altered through folk etymology. However, Black cites one John sine terra (c. 1180–1214), suggesting that the surname could have arisen quite literally as a nickname for a man with no land.
Surname or Lastname
English
English : unexplained. It may be a variant of a medieval name, Preville, a habitational name from a Norman place named with the elements pré ‘meadow’ + ville ‘settlement’. However, this theory is not supported by evidence of early forms.
Surname or Lastname
English
English : according to Reaney this is a nickname from an unattested Old English word cybbe meaning ‘clumsy’ or ‘thickset’. Reaney’s speculation is apparently based on taking the Middle English word kibble ‘cudgel’ as a diminutive of an unattested Old English word. Corresponding personal names have been postulated for the place names Kibworth (‘enclosure of a man called Cybba’) and Kibblesworth (‘enclosure of a man called Cybbel’); so, in theory, the surname could be a reflex of these Old English personal names.North German : nickname for a cantankerous person, from Middle Low German, Middle High German kiven ‘to quarrel’.
Surname or Lastname
English and Scottish
English and Scottish : topographic name for someone who lived by a patch of wet ground overgrown with brushwood, northern Middle English kerr (Old Norse kjarr). A legend grew up that the Kerrs were left-handed, on theory that the name is derived from Gaelic cearr ‘wrong-handed’, ‘left-handed’.Irish : see Carr.This surname has also absorbed examples of German Kehr.
Surname or Lastname
English
English : from a short form of the personal names Giles, Julian, or William. In theory the name would have a soft initial when derived from the first two of these, and a hard one when from William or from the other possibilities discussed in 2–4 below. However, there has been much confusion over the centuries.Northern English : topographic name for someone who lived by a ravine or deep glen, Middle English gil(l), Old Norse gil ‘ravine’.Scottish and Irish : reduced Anglicized form of Gaelic Mac Gille (Scottish), Mac Giolla (Irish), patronymics from an occupational name for a servant or a short form of the various personal names formed by attaching this element to the name of a saint. See McGill. The Old Norse personal name Gilli is probably of this origin, and may lie behind some examples of the name in northern England.Scottish and Irish : reduced Anglicized form of Gaelic Mac An Ghoill (see Gall 1).Norwegian : habitational name from any of three farmsteads in western Norway named Gil, from Old Norse gil ‘ravine’.Dutch : cognate of Giles.Jewish (Israeli) : ornamental name from Hebrew gil ‘joy’.German : from a vernacular short form of the medieval personal name Aegidius (see Gilger).Indian (Panjab) : Sikh name, probably from Panjabi gil ‘moisture’, also meaning ‘prosperity’. There is a Jat tribe that bears this name; the Ramgarhia Sikhs also have a clan called Gill.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : in all probability from the Swale river in Yorkshire. (Reaney and Wilson list a 17th-century example, Swayles, with this origin.) Alternatively, it may be a metronymic from the Old Norse female personal name Svala.
Surname or Lastname
English (mainly Gloucestershire), Dutch, and German (also Türk)
English (mainly Gloucestershire), Dutch, and German (also Türk) : from Middle English, Old French turc, Middle High and Low German Turc ‘Turk’, from Turkish türk. In theory this could be an ethnic name but, both in England and northwest Europe, it is generally a nickname for a person with black hair and a swarthy complexion or a cruel, rowdy, or unruly person. The Dutch and German surname also represents a house name, derived from the use of a picture of a Turk as a house sign. It is also found as a nickname for someone who had taken part in the wars against the Turks.English : from a medieval personal name, a back-formation from Turkel, misanalyzed as containing the Old French diminutive suffix -el.Scottish : reduced Anglicized form of Gaelic Mac Tuirc, a patronymic from the byname Torc ‘boar’.Jewish (Ashkenazic) : ethnic name denoting someone from Turkey or anywhere in the Ottoman Empire, or a nickname for someone thought to resemble a Turk.Americanized form of the Greek ethnic name Tourkos ‘Turk’. See also Turco.
Surname or Lastname
English, Scottish, and Irish (of Norman origin)
English, Scottish, and Irish (of Norman origin) : of disputed origin. It may be from a Celtic personal name derived from the element cam ‘bent’, ‘crooked’ (compare Cameron and Campbell). This was relatively frequent in Norfolk, Lincolnshire, and Yorkshire in the 12th and 13th centuries, perhaps as a result of Breton immigration. According to another theory it is a habitational name from Comines near Lille, but there is no evidence for this (no early forms with de have been found). In southern Ireland this Anglo-Norman name has been confused with 2.Irish : Anglicized form of Gaelic Mac CuimÃn (or Ó CuimÃn) ‘son (or ‘descendant’) of CuimÃn’, a personal name formed from a diminutive of cam ‘crooked’.Americanized form of French Canadian Vien, Viens, based on the misconception that these derive from French venire ‘to come’.
PROBABILITY THEORY
PROBABILITY THEORY
PROBABILITY THEORY
PROBABILITY THEORY
PROBABILITY THEORY
PROBABILITY THEORY
PROBABILITY THEORY
n.
That which is or appears probable; anything that has the appearance of reality or truth.
a.
Presumptive; as, an antecedent improbability.
n.
The doctrine of the probabilists.
n.
The quality or state of being portable; fitness to be carried.
adv.
In all probability; probably.
pl.
of Improbability
adv.
By presumption, or supposition grounded or probability; presumably.
n.
One who maintains that a man may do that which has a probability of being right, or which is inculcated by teachers of authority, although other opinions may seem to him still more probable.
n.
The want of likelihood; improbability.
n.
The quality or state of being probable; appearance of reality or truth; reasonable ground of presumption; likelihood.
n.
Probability.
superl.
Having probability; affording probability; probable; likely.
n.
Probability.
n.
Likelihood of the occurrence of any event in the doctrine of chances, or the ratio of the number of favorable chances to the whole number of chances, favorable and unfavorable. See 1st Chance, n., 5.
n.
Probability; verisimilitude.
n.
Appearance of truth or reality; probability; verisimilitude.
n.
Likelihood; probability.
n.
One who maintains that certainty is impossible, and that probability alone is to govern our faith and actions.
n.
Probability; likelihood.
pl.
of Probability
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