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Property of an irrational number
number theory, specifically in Diophantine approximation theory, the Markov constant M ( α ) {\displaystyle M(\alpha )} of an irrational number α {\displaystyle
Markov_constant
Function that quantifies how near a number is to being rational
f(q,M)=(Mq^{2})^{-1}} gives a stronger irrationality measure: the Markov constant M ( x ) {\displaystyle M(x)} . For an irrational number x ∈ R ∖ Q {\displaystyle
Irrationality_measure
Concept 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 positive constant. Markov's
Markov's_inequality
Solution to x*x + y*y + z*z = 3xyz
A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation x 2 + y 2 + z 2 = 3 x y
Markov_number
Calculation of complex statistical distributions
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution
Markov_chain_Monte_Carlo
Bulgarian dissident writer (1929–1978)
Georgi Ivanov Markov (Bulgarian: Георги Иванов Марков [ɟɛˈɔrɟi ˈmarkov]; 1 March 1929 – 11 September 1978) was a Bulgarian dissident writer. He worked
Georgi_Markov
Mathematical model for sequential decision making under uncertainty
A Markov decision process (MDP) is a mathematical model for sequential decision making when outcomes are uncertain. It is a type of stochastic decision
Markov_decision_process
Memoryless property of a stochastic process
named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of "present"
Markov_property
Complicated set of real numbers
In mathematics, the Markov spectrum, devised by Andrey Markov, is a complicated set of real numbers arising in Markov Diophantine equations and also in
Markov_spectrum
Theorem in number theory that gives a bound on a Diophantine approximation
formula above holds. The theorem is equivalent to the claim that the Markov constant of every number is larger than 5 {\displaystyle {\sqrt {5}}} . Dirichlet's
Hurwitz's theorem (number theory)
Hurwitz's_theorem_(number_theory)
Statistical Model
into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state
Hidden_semi-Markov_model
Rational-number approximation of a real number
quotients. Equivalently, a number is badly approximable if and only if its Markov constant is finite or equivalently its simple continued fraction is bounded
Diophantine_approximation
In probability theory, Kemeny’s constant is the expected number of time steps required for a Markov chain to transition from a starting state i to a random
Kemeny's_constant
Stochastic processes
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both
Gauss–Markov_process
the Markov operator admits a kernel representation. Markov operators can be linear or non-linear. Closely related to Markov operators is the Markov semigroup
Markov_operator
Concept in statistics
statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields
Hidden_Markov_random_field
Class of irrational numbers
number then μ ( x ) = ∞ {\displaystyle \mu (x)=\infty } . Brjuno number Markov constant Diophantine approximation Joseph Liouville (May 1844). "Mémoires et
Liouville_number
DC Comics characters
published by DC Comics. The first Terra, Tara Markov, joins the Teen Titans as a double agent for Deathstroke. Markov was created by Marv Wolfman and George
Terra_(character)
Examples of the probabilistic construct
contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general
Examples_of_Markov_chains
Markov's principle (also known as the Leningrad principle), named after Andrey Markov Jr, is a conditional existence statement for which there are many
Markov's_principle
Theorem related to ordinary least squares
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest
Gauss–Markov_theorem
Sum of the inverses of the positive cubes
(2005), "Infinite families of accelerated series for some classical constants by the Markov-WZ method", Discrete Mathematics & Theoretical Computer Science
Apéry's_constant
Principle in kinetic systems
balance in kinetics seem to be clear. A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary
Detailed_balance
Time required for a Markov chain to reach a stationary distribution
of a Markov chain is the time until the Markov chain is "close" to its steady state distribution. More precisely, a fundamental result about Markov chains
Markov_chain_mixing_time
Dimensionless number that quantifies the strength of the electromagnetic interaction
Webb, J.K.; Murphy, M.T. (2009). "Markov chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy". Memorie
Fine-structure_constant
mathematical theory of Markov chains, the Markov chain tree theorem is an expression for the stationary distribution of a Markov chain with finitely many
Markov_chain_tree_theorem
Equations characterizing continuous-time Markov processes
characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes
Kolmogorov_equations
Generalization of a Markov decision process
A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process
Partially observable Markov decision process
Partially_observable_Markov_decision_process
Special type of irrational number
in fact their difference is bounded by a universal constant. Irrationality measure Markov constant Brjuno, Alexander D. (1971), "Analytic form of differential
Brjuno_number
Lossless compression algorithm
LZMA (Lempel–Ziv–Markov chain algorithm) is a lossless data compression algorithm developed since 1998 by Igor Pavlov, the developer of 7-Zip. It has been
LZMA
Mixing property of Markov chains and graphs
science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time, that is, how rapidly the
Conductance_(graph_theory)
Collection of random variables
scientists. Markov processes and Markov chains are named after Andrey Markov who studied Markov chains in the early 20th century. Markov was interested
Stochastic_process
Bound on probability of a random variable being far from its mean
also refer to Markov's inequality, especially in the context of analysis. They are closely related, and some authors refer to Markov's inequality as "Chebyshev's
Chebyshev's_inequality
Overview of and topical guide to probability
dominated convergence theorems Markov's inequality and Chebyshev's inequality Independent random variables Discrete: constant (see also degenerate distribution)
Outline_of_probability
Mathematical theorem
distribution can be represented as events generated by a Markov network (also known as a Markov random field). It is the fundamental theorem of random fields
Hammersley–Clifford_theorem
Statistics concept
no longer a renewal process. Rather, a Markov renewal process is used. In the case that we have only two Markov states with equal transition probabilities
Fano_factor
Constant in Riemannian geometry
analysis, but also in the theory of Markov chains and in graph theory, where they have inspired the analogous Cheeger constant of a graph and the notion of conductance
Cheeger_constant
Simulation method in statistics
In computational statistics, reversible-jump Markov chain Monte Carlo is an extension to standard Markov chain Monte Carlo (MCMC) methodology, introduced
Reversible-jump Markov chain Monte Carlo
Reversible-jump_Markov_chain_Monte_Carlo
R. Finch, Mathematical Constants, §2.31.3 "Markov–Hurwitz Equation" (2003), p. 200. Aigner, Martin (July 18, 2013). Markov's Theorem and 100 Years of
Square_root_of_8
Lossless data compression algorithm
Dynamic Markov compression (DMC) is a lossless data compression algorithm developed by Gordon Cormack and Nigel Horspool. It uses predictive arithmetic
Dynamic_Markov_compression
Mathematical concept
widespread problems outside of physics, such as Hopfield networks, Markov networks, Markov logic networks, and boundedly rational potential games in game
Gibbs_measure
Natural number
companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a Markov number. 34 is also the fourth heptagonal number, and the first non-trivial
34_(number)
Monte Carlo algorithm
sampler, also known in statistical mechanics as the heat bath algorithm, is a Markov chain Monte Carlo (MCMC) algorithm for sampling from a specified multivariate
Gibbs_sampling
Model of asset returns
are constants and { ϵ t {\displaystyle \epsilon _{t}} } are independent standard Gaussians. Volatility is driven by the first-order latent Markov state
Markov_switching_multifractal
)} such that X 0 {\displaystyle X_{0}} is constant with probability one. If X {\displaystyle X} has Markov property with respect to the filtration { F
Blumenthal's_zero–one_law
Topics referred to by the same term
management module, a term in color management Conditional Markov model or maximum-entropy Markov model Coordinate-measuring machine, a device for dimensional
CMM
Mathematics concept
In mathematics, the Chvátal–Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings. Although
Chvátal–Sankoff_constants
random walk Markov chain Examples of Markov chains Detailed balance Markov property Hidden Markov model Maximum-entropy Markov model Markov chain mixing
List_of_probability_topics
Measure of whether or not a graph has a "bottleneck"
In mathematics, the Cheeger constant (also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck"
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
isomorphic; these include many finite stationary stochastic processes, including Markov chains and subshifts of finite type, Anosov flows and Sinai's billiards
Ornstein_isomorphism_theorem
Generative AI chatbot by OpenAI
it for". The Washington Post. Gao, Catherine A.; Howard, Frederick M.; Markov, Nikolay S.; Dyer, Emma C.; Ramesh, Siddhi; Luo, Yuan; Pearson, Alexander
ChatGPT
Engineering formula
deterioration modeling. Recently, more complex methods based on simulation, Markov models and machine learning models have been introduced. A well-known model
Deterioration_modeling
Series of activities
integrated development environment In probability theory: Branching process, a Markov process that models a population Diffusion process, a solution to a stochastic
Process
Class of statistical modeling methods
{Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent
Conditional_random_field
Mathematical proof technique
binary quadratic forms. For example, it was used in the analysis of the Markov equation back in 1879 and in the 1953 paper of Mills. In 1988, the method
Vieta_jumping
Representation of a type of random process
widely applied in cases where the underlying dynamics of the system are not constant, such as in sensors time series modelling, climate science, economics and
Autoregressive_model
German historian
Walter Karl Hugo Markov (born Mulec; 5 October 1909 – 3 July 1993) was a German historian. Shortly after he received his doctorate, a promising academic
Walter_Markov
1943 Soviet comedy film
Pyotr Nikolayevich Markov, who is recovering from an eye injury. Unbeknownst to her, Markov is Agafya’s son. As they grow closer, Markov confides his deep
Actress_(1943_film)
Stochastic volatility model used in derivatives markets
<1} : d W t d Z t = ρ d t {\displaystyle dW_{t}\,dZ_{t}=\rho \,dt} The constant parameters β , α {\displaystyle \beta ,\;\alpha } satisfy the conditions
SABR_volatility_model
GK Wilhelmus Martinus van Eeck 1893-03-13 19 0 GVC Wageningen 0 0 - DF Constant Feith 1884-08-03 27 6 HVV Den Haag 2 0 - MF Ge Fortgens 1887-07-10 24 6
Football at the 1912 Summer Olympics – Men's team squads
Football_at_the_1912_Summer_Olympics_–_Men's_team_squads
Generating pseudo-random numbers that follow a probability distribution
distributions): Markov chain Monte Carlo, the general principle Metropolis–Hastings algorithm Gibbs sampling Slice sampling Reversible-jump Markov chain Monte
Non-uniform random variate generation
Non-uniform_random_variate_generation
Average uncertainty in variable's states
encrypted at all. A common way to define entropy for text is based on the Markov model of text. For an order-0 source (each character is selected independent
Entropy_(information_theory)
Stochastic matrix representing links between entities
matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed from A by dividing the elements of
Google_matrix
Time at which a random variable stops exhibiting a behavior of interest
particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type
Stopping_time
Technique for setting initial values of trainable parameters in a neural network
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Weight_initialization
Statistical method
convex optimization. Where the steps can be modelled as a Markov chain, then Hidden Markov Models are also often used (a popular approach in the biophysics
Step_detection
In mathematics, the Markov–Kakutani fixed-point theorem, named after Andrey Markov and Shizuo Kakutani, states that a commuting family of continuous affine
Markov–Kakutani fixed-point theorem
Markov–Kakutani_fixed-point_theorem
Hungarian-American mathematician and computer scientist (1926–1992)
J.: Prentice-Hall. Kemeny method Kemeny's constant (an invariant sum arising in the study of finite Markov chains). New Hampshire Historical Marker No
John_G._Kemeny
property, Markov's inequality, Markov processes, Markov random field, Markov algorithm etc. Andrey Markov, Jr., author of Markov's principle and Markov's rule
List of Russian mathematicians
List_of_Russian_mathematicians
Measure of algorithmic complexity
almost all x {\displaystyle x} . It can be shown that for the output of Markov information sources, Kolmogorov complexity is related to the entropy of
Kolmogorov_complexity
Stochastic Markov process
A Brownian snake is a stochastic Markov process on the space of stopped paths. It has been extensively studied., and was in particular successfully used
Brownian_snake
More specifically, PSL uses "soft" logic as its logical component and Markov random fields as its statistical model. PSL provides sophisticated inference
Probabilistic_soft_logic
Solution to a stochastic differential equation
theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion processes
Diffusion_process
Property of measure-preserving dynamical systems
ergodic for the shift map. Another important case is that of a stationary Markov chain, which is discussed in detail below. A similar interpretation holds
Ergodicity
Generalization of the concept from statistical mechanics
corpus linguistics and artificial intelligence, which employ Markov networks, and Markov logic networks. The Gibbs measure is also the unique measure
Partition function (mathematics)
Partition_function_(mathematics)
Mathematical models of changing DNA
A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe
Models_of_DNA_evolution
Situation where total gains match total losses
optimal is called a conflict game. Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero. Such games are
Zero-sum_game
Gauss–Kuzmin distribution, a discrete probability distribution Gauss–Markov process Gauss–Markov theorem Gaussian copula Gaussian measure Gaussian correlation
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
Natural number
thirteen primes 6441 – triangular number 6449 – Sophie Germain prime 6466 – Markov number 6480 – smallest number with exactly 50 factors 6491 – Sophie Germain
6000_(number)
For an infinite buffer with constant service rate μ and arrivals at rates λ and 0, modulated by a continuous time Markov chain with parameters Q = ( −
Fluid_queue
Property of a thermodynamic system
that may change during experiment. Entropy can also be defined for any Markov processes with reversible dynamics and the detailed balance property. In
Entropy
Number measuring the chance an event occurs
improved the exposition of the theory. In 1906, Andrey Markov introduced the notion of Markov chains, which played an important role in stochastic processes
Probability
Sampling algorithm
Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random samples whose
Hamiltonian_Monte_Carlo
Quantum variations of random walks
walks is through continuous-time Markov chains. Unlike the coin-based mechanism used in discrete-time random walks, Markov chains do not rely on a coin flip
Quantum_walk
Algorithm that estimates unknowns from a series of measurements over time
be an unobserved Markov process, and the measurements are the observed states of a hidden Markov model (HMM). Because of the Markov assumption, the true
Kalman_filter
Method for estimating the unknown parameters in a linear regression model
the residuals when regressors have finite fourth moments and—by the Gauss–Markov theorem—optimal in the class of linear unbiased estimators when the errors
Ordinary_least_squares
Weisstein, Eric W. "Khinchin's Constant". mathworld.wolfram.com. Retrieved 2024-09-22. Aigner, Martin (2013). Markov's theorem and 100 years of the uniqueness
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Process forming a path from many random steps
+ b ) {\displaystyle O(a+b)} in the general one-dimensional random walk Markov chain. Some of the results mentioned above can be derived from properties
Random_walk
Method of sampling from a Markov chain
Among Markov chain Monte Carlo (MCMC) algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary
Coupling_from_the_past
Averages of repeated trials converge to the expected value
to refinement of the law, including Chebyshev, Markov, Borel, Cantelli, Kolmogorov and Khinchin. Markov showed that the law can apply to a random variable
Law_of_large_numbers
computational statistics, the preconditioned Crank–Nicolson algorithm (pCN) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples – sequences
Preconditioned Crank–Nicolson algorithm
Preconditioned_Crank–Nicolson_algorithm
Stochastic process
Progressively measurable process Wiliams, David (1979). "II.25". Diffusions, Markov Processes and Martingales: Foundations. Vol. 1. Wiley. ISBN 0-471-99705-6
Adapted_process
Technique of using algorithms to create music
possibilities of random events. Prominent examples of stochastic algorithms are Markov chains and various uses of Gaussian distributions. Stochastic algorithms
Algorithmic_composition
Set of cryptographic hash functions
IACR. Stevens, Marc; Bursztein, Elie; Karpman, Pierre; Albertini, Ange; Markov, Yarik. The first collision for full SHA-1 (PDF) (Technical report). Google
SHA-2
Empirical law on the variance of species in a habitat
variance function. As a response to this model Taylor argued that such a Markov process would predict that the power law exponent would vary considerably
Taylor's_law
Natural number
725 = number of centered hydrocarbons with 28 carbon atoms 321,534,781 = Markov prime 331,160,281 = Leonardo prime 336,849,900 = number of primitive polynomials
100,000,000
transition matrix of a finite-state, discrete-time, reversible stationary Markov chain. It can be seen as a special case of Cheeger inequalities in expander
Cheeger_bound
Soviet mathematician (1907–1989)
had a difficult academic career, not completing his first degree and constantly being troubled by antisemitic discrimination. His supervisor was Nikolai
Mark_Krein
Approximation method in statistics
least-squares estimator. An extended version of this result is known as the Gauss–Markov theorem. The idea of least-squares analysis was also independently formulated
Least_squares
Probability distribution
describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases.
Phase-type_distribution
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