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...tion source]] whose underlying dynamics are given by a stationary finite [[Markov chain]]. A Markov information source is then a (stationary) Markov chain <math>M</math>, together with a [[Function (mathematics)|function]] ...

...y to HMM, the state transition process in TI-HBM is not a [[Markov process|Markov-dependent process]], rather it is a [[Bernoulli scheme|generalized Bernoull ...rkov: Investigation of state transition regime in switching-state acoustic models," ''Signal Processing'', vol. 89, no. 4, pp. 662–668, April 2009. ...

...mization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes | journal = Operations Research | volume = 32 | issue = 2 | pages ...2-0}}</ref><ref name="ross">{{cite book |title=Introduction to probability models|last=Ross |first=Sheldon M. |year=2007 |publisher=Academic Press |isbn=0-12 ...

=== In terms of Markov kernels=== ...compose]]. Given a [[measurable space]] <math>(X,\mathcal{A})</math> and a Markov kernel <math>k:(X,\mathcal{A})\to(X,\mathcal{A})</math>, the ''two-step tra ...

...s for Computing Stationary Distributions of Nearly Completely Decomposable Markov Chains | journal = [[SIAM Journal on Algebraic and Discrete Methods]] | vol A [[Markov chain]] with [[Stochastic matrix|transition matrix]] ...

...method for reducing the size of the state space of some [[continuous-time Markov chain]]s, first published by [[John George Kemeny|Kemeny]] and Snell.<ref> | title = Finite Markov Chains ...

...e mathematical theory of [[stochastic processes|random processes]], the '''Markov chain central limit theorem''' has a conclusion somewhat similar in form to ...om element]]s of some set is a [[Markov chain]] that has a [[Discrete-time Markov chain#Stationary distributions|stationary probability distribution]]; and ...

'''Construction of an irreducible Markov Chain''' is a mathematical method used to prove results related the changin ...when achieving exact [[Goodness-of-fit test|goodness-of-fit tests]] with [[Markov chain Monte Carlo]] (MCMC) methods. ...

...2 = Dayne|last3 = Pereira|first3 = Fernando|title = Maximum Entropy Markov Models for Information Extraction and Segmentation|book-title = Proc. ICML 2000|ye ...mid O_1, \dots, O_n)</math>. In a MEMM, this probability is factored into Markov transition probabilities, where the probability of transitioning to a parti ...

...s databases 57 (2004): 1-22.</ref> Probabilistic methods based on [[hidden Markov model]]s have also proved useful in solving this problem.<ref>[[Emily B. Fo ===Hidden Markov Models=== ...

A '''dependability state diagram''' is a method for modelling a system as a [[Markov chain]]. It is used in [[reliability engineering]] for availability and rel Finite state models of systems are subject to [[State explosion problem|state explosion]]. To c ...

...ole that the [[Stochastic matrix|transition matrix]] does in the theory of Markov processes with a [[finite set|finite]] [[state space]].<ref>{{Cite book | l ...al A)</math> and <math>(Y,\mathcal B)</math> be [[measurable space]]s. A ''Markov kernel'' with source <math>(X,\mathcal A)</math> and target <math>(Y,\mathc ...

...mirni | first2 = E. | author2-link = Evgenia Smirni | chapter = M/G/1-Type Markov Processes: A Tutorial | doi = 10.1007/3-540-45798-4_3 | title = Performance ...hor|date=2024-06-13|bot=User:Cewbot/log/20201008/configuration|target_link=Markov chain#Reducibility|reason= The anchor (Reducibility) [[Special:Diff/9706941 ...

...lar to commonly used supervised learning techniques, structured prediction models are typically trained by means of observed data in which the predicted valu ...m, A. |author3=Pereira, F. |title=Conditional random fields: Probabilistic models for segmenting and labeling sequence data|book-title =Proc. 18th Internatio ...

'''Dependency networks (DNs)''' are [[graphical model]]s, similar to [[Markov network]]s, wherein each vertex (node) corresponds to a random variable and ==Markov blanket== ...

{{Short description|Equations characterizing continuous-time Markov processes}} ...]es. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes over time. ...

...014|loc=birth-and-death process}} is a special case of a [[continuous-time Markov process]] and a generalisation of a [[Poisson process]]. It defines a conti ===Continuous-time Markov chain definition=== ...

...te models''' ('''ALAAMs''') are a group of [[Statistical model|statistical models]] designed to analyze how traits or characteristics (node attributes) of in ...d social struc-tures: a social selection model. ''Exponential Random Graph Models for Social Networks: Theory, Methods and Applications. Cambridge University ...

...<math> S </math>. More precisely IPS are continuous-time [[Markov process|Markov jump processes]] describing the collective behavior of stochastically inter ...esses)|Markov generator]] giving rise to a unique [[Markov process]] using Markov [[semigroups]] and the [[Hille-Yosida theorem]]. The generator again is giv ...

...n Haykin]]. {{ISBN|0-471-22154-6}}</ref> but related switching state-space models have been in use. ...]], [[Geoffrey E. Hinton]]. Variational Learning for Switching State-Space Models. Neural Computation, 12(4):963–996.</ref> ...