###### **Markov** **chain**

Hidden

**Markov**model**Markov**blanket**Markov****chain**geostatistics**Markov****chain**mixing time**Markov****chain**Monte Carlo**Markov**decision ... process**Markov**information source**Markov**random field Quantum**Markov****chain**Telescoping**Markov****chain**Variable-order**Markov**model ... A beautiful visual explanation of**Markov****Chains**Chapter 5:**Markov****Chain**Models Making Sense and Nonsense of**Markov****Chains**... A**Markov****chain**is a stochastic process with the**Markov**property. The term "**Markov****chain**" refers to the sequence of random ...###### Examples of **Markov** **chains**

A game of snakes and ladders or any other game whose moves are determined entirely by dice is a

**Markov****chain**, indeed, an ... Google's PageRank algorithm is essentially a**Markov****chain**over the graph of the Web.[not in citation given] Mark V. Shaney ... ISBN 978-1-119-38755-8. Gagniuc, Paul A. (2017).**Markov****Chains**: From Theory to Implementation and Experimentation. USA, NJ: ... This page contains examples of**Markov****chains**in action. ... absorbing**Markov****chain**. This is in contrast to card games such ...###### Additive **Markov** **chain**

In probability theory, an additive

**Markov****chain**is a**Markov****chain**with an additive conditional probability function. Here the ... A binary additive**Markov****chain**is where the state space of the**chain**consists on two values only, Xn ∈ { x1, x2 }. For example ... Examples of**Markov****chains**S.S. Melnyk, O.V. Usatenko, and V.A. Yampol'skii. (2006) "Memory functions of the additive**Markov**... An additive**Markov****chain**of order m is a sequence of random variables X1, X2, X3, ..., possessing the following property: the ...###### Absorbing **Markov** **chain**

In an absorbing

**Markov****chain**, a state that is not absorbing is called transient. Let an absorbing**Markov****chain**with transition ... 3: Absorbing**Markov****Chains**". In Gehring, F. W.; Halmos, P. R. Finite**Markov****Chains**(Second ed.). New York Berlin Heidelberg ... Like general**Markov****chains**, there can be continuous-time absorbing**Markov****chains**with an infinite state space. However, this ... In the mathematical theory of probability, an absorbing**Markov****chain**is a**Markov****chain**in which every state can reach an ...###### Quantum **Markov** **chain**

In mathematics, the quantum

**Markov****chain**is a reformulation of the ideas of a classical**Markov****chain**, replacing the classical ... More precisely, a quantum**Markov****chain**is a pair ( E , ρ ) {\displaystyle (E,\rho )} with ρ {\displaystyle \rho } a density ... Very roughly, the theory of a quantum**Markov****chain**resembles that of a measure-many automaton, with some important ... "Quantum**Markov****chains**." Journal of Mathematical Physics 49.7 (2008): 072105.. ...###### Telescoping **Markov** **chain**

In probability theory, a telescoping

**Markov****chain**(TMC) is a vector-valued stochastic process that satisfies a**Markov**property ... is a**Markov****chain**with transition probability matrix Λ 1 {\displaystyle \Lambda ^{1}} P ( θ k 1 = s , θ k − 1 1 = r ) = Λ 1 ( s ... satisfies a**Markov**property with a transition kernel that can be written in terms of the Λ {\displaystyle \Lambda } 's, P ( θ k ...###### **Markov** **chain** geostatistics

A

**Markov****chain**random field is still a single spatial**Markov****chain**. The spatial**Markov****chain**moves or jumps in a space and ...**Markov****chain**geostatistics uses**Markov****chain**spatial models, simulation algorithms and associated spatial correlation measures ... e.g., transiogram) based on the**Markov****chain**random field theory, which extends a single**Markov****chain**into a multi-dimensional ... is proposed as the accompanying spatial measure of**Markov****chain**random fields. Li, W. 2007.**Markov****chain**random fields for ...###### **Markov** **chain** mixing time

In probability theory, the mixing time of a

**Markov****chain**is the time until the**Markov****chain**is "close" to its steady state ... More precisely, a fundamental result about**Markov****chains**is that a finite state irreducible aperiodic**chain**has a unique ... Such problems can, for sufficiently large number of colors, be answered using the**Markov****chain**Monte Carlo method and showing ... Mixing (mathematics) for a formal definition of mixing Aldous, David; Fill, Jim, Reversible**Markov****Chains**and Random Walks on ...###### **Markov** **chain** approximation method

In case of need, one must as well approximate the cost function for one that matches up the

**Markov****chain**chosen to approximate ... F. B. Hanson, "**Markov****Chain**Approximation", in C. T. Leondes, ed., Stochastic Digital Control System Techniques, Academic Press ... In numerical methods for stochastic differential equations, the**Markov****chain**approximation method (MCAM) belongs to the several ... The basic idea of the MCAM is to approximate the original controlled process by a chosen controlled**markov**process on a finite ...###### **Markov** **chain** Monte Carlo

These interacting

**Markov****chain**Monte Carlo samplers can be interpreted as a way to run in parallel a sequence of**Markov****chain**... In principle, any**Markov****chain**Monte Carlo sampler can be turned into an interacting**Markov****chain**Monte Carlo sampler. ... Random walk Monte Carlo methods make up a large subclass of**Markov****chain**Monte Carlo methods.**Markov****chain**Monte Carlo methods ... In contrast to traditional**Markov****chain**Monte Carlo methods, the precision parameter of this class of interacting**Markov****chain**...###### Nearly completely decomposable **Markov** **chain**

In probability theory, a nearly completely decomposable (NCD)

**Markov****chain**is a**Markov****chain**where the state-space can be ... A**Markov****chain**with transition matrix P = ( 1 2 1 2 0 0 1 2 1 2 0 0 0 0 1 2 1 2 0 0 1 2 1 2 ) + ϵ ( − 1 2 0 1 2 0 0 − 1 2 0 1 2 ... Example 1.1 from Yin, George; Zhang, Qing (2005). Discrete-time**Markov****chains**: two-time-scale methods and applications. ... Particularly efficient algorithms exist to compute the stationary distribution of**Markov****chains**with this property. Ando and ...###### Lempel-Ziv-**Markov** **chain** algorithm

LZMA uses

**Markov****chains**, as implied by "M" in its name. The binary tree approach follows the hash**chain**approach, except that ... The Lempel-Ziv-**Markov****chain**algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been under ... the search stop after a pre-defined number of hash**chain**nodes has been traversed, or when the hash**chains**"wraps around", ...**Chaining**is achieved by an additional array which stores, for every dictionary position, the last seen previous position whose ...###### **Markov** **chains** on a measurable state space

A

**Markov****chain**on a measurable state space is a discrete-time-homogenous**Markov****chain**with a measurable space as state space. ... The definition of**Markov****chains**has evolved during the 20th century. In 1953 the term**Markov****chain**was used for stochastic ... Sean Meyn and Richard L. Tweedie:**Markov****Chains**and Stochastic Stability. 2nd edition, 2009. Daniel Revuz:**Markov****Chains**. 2nd ... denotes the**Markov****chain**according to a**Markov**kernel p {\displaystyle p} with stationary measure μ {\displaystyle \mu } , then ...###### Reversible-jump **Markov** **chain** Monte Carlo

In computational statistics, reversible-jump

**Markov****chain**Monte Carlo is an extension to standard**Markov****chain**Monte Carlo ( ... Green, P.J. (1995). "Reversible Jump**Markov****Chain**Monte Carlo Computation and Bayesian Model Determination". Biometrika. 82 (4 ...###### Construction of an irreducible **Markov** **chain** in the Ising model

**Markov**

**Chain**in the Ising model is the first step in overcoming a computational obstruction encountered when a

**Markov**

**chain**... So we an get the irreducibility of the

**Markov**

**Chain**based on simple swaps for the 1-dimension Ising model. Even though we just ... Then the

**Markov**basis in Ising model can be degined as: A

**Markov**bases for the Ising model is a set Z ~ ⊂ Z N 1 × ⋯ × N d {\ ... Thus in the following we will show how to modify the algorithm mentioned in the paper to get the irreducible

**Markov**

**chain**in ...

###### Fork-join queue

"

**Markov****Chains**". Basics of Applied Stochastic Processes. Probability and Its Applications. doi:10.1007/978-3-540-89332-5_1. ISBN ...###### Transition rate matrix

Norris, J. R. (1997). "

**Markov****Chains**". doi:10.1017/CBO9780511810633. ISBN 9780511810633. ... Passage Times for**Markov****Chains**. IOS Press. doi:10.3233/978-1-60750-950-9-i. ISBN 90-5199-060-X. Asmussen, S. R. (2003). " ... weighted graph whose vertices correspond to the**Markov****chain's**states. An M/M/1 queue, a model which counts the number of jobs ... is an array of numbers describing the rate a continuous time**Markov****chain**moves between states. In a transition rate matrix Q ( ...###### Time reversibility

Kolmogorov's criterion defines the condition for a

**Markov****chain**or continuous-time**Markov****chain**to be time-reversible. Time ...**Markov****chains**, and piecewise deterministic**Markov**processes. Time reversal method works based on the linear reciprocity of the ... Norris, J. R. (1998).**Markov****Chains**. Cambridge University Press. ISBN 0521633966. Löpker, A.; Palmowski, Z. (2013). "On time ...**Markov**processes can only be reversible if their stationary distributions have the property of detailed balance: p ( x t = i , ...###### Balance equation

... of a

**Markov****chain**, when such a distribution exists. For a continuous time**Markov****chain**with state space S, transition rate from ... For a continuous time**Markov****chain**(CTMC) with transition rate matrix Q, if π i {\displaystyle \pi _{i}} can be found such that ... In probability theory, a balance equation is an equation that describes the probability flux associated with a**Markov****chain**in ... For a discrete time**Markov****chain**with transition matrix Q and equilibrium distribution π {\displaystyle \pi } , the global ...###### James R. Norris

Norris, J. R. (1997).

**Markov****Chains**. Cambridge University Press. "James Norris's homepage at Cambridge University". "James ...###### Foster's theorem

It uses the fact that positive recurrent

**Markov****chains**exhibit a notion of "Lyapunov stability" in terms of returning to any ... Consider an irreducible discrete-time**Markov****chain**on a countable state space S having a transition probability matrix P with ... Brémaud, P. (1999). "Lyapunov Functions and Martingales".**Markov****Chains**. p. 167. doi:10.1007/978-1-4757-3124-8_5. ISBN 978-1- ... Foster's theorem states that the**Markov****chain**is positive recurrent if and only if there exists a Lyapunov function V : S → R ...###### Kemeny's constant

... required for a

**Markov****chain**to transition from a starting state i to a random destination state sampled from the**Markov****chain's**... It is in that sense a constant, although it is different for different**Markov****chains**. When first published by John Kemeny in ... For a finite ergodic**Markov****chain**with transition matrix P and invariant distribution π, write mij for the mean first passage ... Kemeny, J. G.; Snell, J. L. (1960). Finite**Markov****Chains**. Princeton, NJ: D. Van Nostrand. (Corollary 4.3.6) Catral, M.; ...###### Hydrological modelling

**Markov**

**Chains**are a mathematical technique for determine the probability of a state or event based on a previous state or event ...

**Markov**

**Chains**were first used to model rainfall event length in days in 1976, and continues to be used for flood risk ... "

**Markov**

**Chains**explained visually". Explained Visually. Retrieved 2017-04-21. Haan, C. T.; Allen, D. M.; Street, J. O. (1976-06- ... "A

**Markov**

**Chain**Model of daily rainfall". Water Resources Research. 12 (3): 443-449. Bibcode:1976WRR....12..443H. doi:10.1029/ ...

###### Entropy (information theory)

See

**Markov****chain**. Entropy is one of several ways to measure diversity. Specifically, Shannon entropy is the logarithm of 1D, ... For a second order**Markov**source, the entropy rate is H ( S ) = − ∑ i p i ∑ j p i ( j ) ∑ k p i , j ( k ) log 2 p i , j ( k ... 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 ... For a first-order**Markov**source (one in which the probability of selecting a character is dependent only on the immediately ...###### Probabilistic bisimulation

Finite

**Markov****Chains**(Second ed.). New York Berlin Heidelberg Tokyo: Springer-Verlag. p. 224. ISBN 978-0-387-90192-3. Oliveira ... When applied to**Markov****chains**, probabilistic bisimulation is the same concept as lumpability. Probabilistic bisimulation ...