Probability Concept
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A Probability Concept is a statistical concept within the probability subject area.
- Context:
- It can (typically) be the referent of a Probability Term.
- It can (typically) be expressed in a Mathematical Language.
- Example(s):
- Counter-Example(s):
- See: Statistician, Categorical Data Analysis.
References
2016
- http://wikipedia.org/wiki/List_of_probability_topics
- General aspects
- Probability; Randomness, Pseudorandomness, Quasirandomness; Randomization, hardware random number generator; Random number generator; Random sequence; Uncertainty; Statistical dispersion; Observational error; Equiprobable; Average; Probability interpretations; Markovian; Statistical regularity; Central tendency; Bean machine; Relative frequency; Frequency probability; Maximum likelihood; Bayesian probability; Principle of indifference; Credal set; Cox's theorem; Principle of maximum entropy; Information entropy; Urn problems; Extractor; Aleatoric, aleatoric music; Free probability; Exotic probability; Schrödinger method; Empirical measure; Glivenko–Cantelli theorem; Zero-one law; Law of Truly Large Numbers; Littlewood–Offord problem; Inclusion-exclusion principle; Impossible event; Information geometry; Talagrand's concentration inequality.
- Foundations of probability theory
- Probability theory; Probability space (Sample space, Standard probability space, Random element, Dynkin system); Probability axioms; Normalizing constant; Event (probability theory) (Complementary event); Elementary event; Mutually exclusive; Boole's inequality; Probability density function; Cumulative distribution function; Law of total cumulance; Law of total expectation; Law of total probability; Law of total variance; Almost surely; Cox's theorem; Bayesianism; Prior probability; Posterior probability; Borel's paradox; Bertrand's paradox; Coherence (philosophical gambling strategy); Dutch book; Algebra of random variables; Belief propagation; Transferable belief model; Dempster–Shafer theory; Possibility theory.
- Random variables.
- Discrete random variable (Probability mass function); Constant random variable; Expected value (Jensen's inequality); Variance (Standard deviation, Geometric standard deviation); Multivariate random variable (Joint probability distribution, Marginal distribution, Kirkwood approximation); Independent identically-distributed random variables (Independent and identically-distributed random variables); Statistical independence (Conditional independence, Pairwise independence, Covariance, Covariance matrix, De Finetti's theorem); Correlation (Uncorrelated, Correlation function); Canonical correlation; Convergence of random variables (Weak convergence of measures, Skorokhod's representation theorem, Lévy's continuity theorem, Uniform integrability); Markov's inequality; Chebyshev's inequality = Chernoff bound; Chernoff's inequality; Bernstein inequalities (probability theory) (Hoeffding's inequality); Kolmogorov's inequality; Etemadi's inequality; Khintchine inequality; Paley–Zygmund inequality; Laws of large numbers (Asymptotic equipartition property, Typical set, Law of large numbers, Kolmogorov's two-series theorem); Random field (Conditional random field); Borel–Cantelli lemma; Wick product.
- Conditional probability.
- Conditioning (probability); Conditional expectation; Conditional probability distribution; Regular conditional probability; Disintegration theorem; Bayes' theorem; de Finetti's theorem (Exchangeable random variables); Rule of succession; Conditional independence; Conditional event algebra (Goodman–Nguyen–van Fraassen algebra)
- Theory of probability distributions
- Probability distribution; Probability distribution function; Probability density function; Probability mass function; Cumulative distribution function; Quantile; Moment (mathematics) (Moment about the mean, Standardized moment, Cumulant, Factorial moment, Expected value, Second moment method, Variance, Covariance function, An inequality on location and scale parameters, Taylor expansions for the moments of functions of random variables, Moment problem); Prior probability distribution; Total variation distance; Hellinger distance; Wasserstein metric; Lévy–Prokhorov metric (Lévy metric); Continuity correction; Heavy-tailed distribution; Truncated distribution; Infinite divisibility; Stability (probability); Indecomposable distribution; Power law; Anderson's theorem; Probability bounds analysis; Probability box.
- Properties of probability distributions
- Central limit theorem (Illustration of the central limit theorem, Concrete illustration of the central limit theorem, Berry–Esséen theorem, Berry–Esséen theorem, De Moivre–Laplace theorem, Lyapunov's central limit theorem, Martingale central limit theorem, Infinite divisibility (probability), Method of moments (probability theory), Stability (probability), Stein's lemma); Characteristic function (probability theory) (Lévy continuity theorem); Edgeworth series; Helly–Bray theorem; Location parameter; Maxwell's theorem; Moment-generating function (Factorial moment generating function); Negative probability; Probability-generating function; Vysochanskiï–Petunin inequality; Mutual information; Kullback–Leibler divergence; Normally distributed and uncorrelated does not imply independent; Le Cam's theorem; Large deviations theory (Contraction principle (large deviations theory), Varadhan's lemma, Tilted large deviation principle, Rate function, Laplace principle (large deviations theory), Exponentially equivalent measures, Cramér's theorem (second part)
- Applied probability.
- Empirical findings (Benford's law, Pareto principle, Zipf's law); Boy or Girl paradox.
- Stochastic processes
- Adapted process; Basic affine jump diffusion; Bernoulli process (Bernoulli scheme); Branching process; Point process; Chapman–Kolmogorov equation; Chinese restaurant process; Coupling (probability); Ergodic theory (Maximal ergodic theorem, Ergodic (adjective)); Galton–Watson process; Gauss–Markov process; Gaussian process (Gaussian random field, Gaussian isoperimetric inequality, Large deviations of Gaussian random functions); Girsanov's theorem; Increasing process; Itô's lemma; Jump diffusion; Law of the iterated logarithm; Lévy flight; Lévy process; Loop-erased random walk; Markov chain (Examples of Markov chains, Detailed balance, Markov property, Hidden Markov model, Maximum-entropy Markov model, Markov chain mixing time); Markov partition; Markov process (Continuous-time Markov process, Piecewise-deterministic Markov process); Martingale (Doob martingale, Optional stopping theorem, Martingale representation theorem, Azuma's inequality, Wald's equation); Poisson process (Poisson random measure); Population process; Process with independent increments; Progressively measurable process; Queueing theory (Erlang unit); Random walk; Random walk Monte Carlo; Renewal theory; Skorokhod's embedding theorem; Stationary process; Stochastic calculus (Itô calculus, Malliavin calculus, Stratonovich integral); Time series analysis (Autoregressive model, Moving average model, Autoregressive moving average model, Autoregressive integrated moving average model, Anomaly time series); Voter model; Wiener process (Brownian motion, Geometric Brownian motion, Donsker's theorem, Empirical process, Wiener equation, Wiener sausage)
- Geometric probability
- Gambling.
- Luck; Game of chance; Odds; Gambler's fallacy; Inverse gambler's fallacy; Parrondo's paradox; Pascal's wager; Gambler's ruin; Poker probability (Poker probability (Omaha), Poker probability (Texas hold 'em), Pot odds); Roulette (Martingale (betting system), The man who broke the bank at Monte Carlo); Lottery (Lottery machine, Pachinko); Coherence (philosophical gambling strategy); Coupon collector's problem.
- Coincidence
- Algorithmics
- Probable prime; Probabilistic algorithm = Randomised algorithm; Monte Carlo method; Las Vegas algorithm; Probabilistic Turing machine; Stochastic programming; Probabilistically checkable proof; Box–Muller transform; Metropolis algorithm; Gibbs sampling; Inverse transform sampling method; Walk-on-spheres method.
- Financial mathematics.
- Genetics.
- General aspects