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Topic: Examples of Markov chains

Related Topics

Hidden Markov model

Markov chain

Markov process

Stochastic matrix

Transition matrix

Martingale

Branching process

Snakes and ladders

Stochastic process

Eigenvalue

Random walk

Andrei Andreevich Markov

Poisson process

Brownian motion

Random walk Monte Carlo

	Examples of Markov chains - Wikipedia, the free encyclopedia
		In this example, predictions for the weather on more distant days are increasingly inaccurate and tend towards a steady state vector.
		For the most prolific example of the use of Markov chains, see Google.
		A description behind the page rank algorithm, which is basically a Markov chain over the graph of the Internet, can be found in the seminal paper, "The Page Rank Citation Ranking: Bringing Order to the Web" by Larry Page, Sergey Brin, R. Motwani, and T. Winograd.
	en.wikipedia.org /wiki/Examples_of_Markov_chains (556 words)

	Markov chain - Wikipedia, the free encyclopedia
		These kinds of discrete finite Markov chains can also be described by a directed graph, where the edges are labeled by the probabilities of going from one state to the other state that are on either end of the directed edge.
		Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events.
		Markov chains also have many applications in biological modelling, particularly population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
	en.wikipedia.org /wiki/Markov_chain (1783 words)

	Markov Chains
		A Markov chain, named in honor of Russian mathematician Andrei Markov, is a stochastic process.
		The interesting thing about this chain is that when d is large and when the Markov chain runs for a long time, there would most likely be approximately d/2 balls in Urn 1.
		Markov chains also have many biological applications, particularly population processes, which are useful in modelling processes that are, at least, analogous to biological populations.
	cs.bilgi.edu.tr /~bulent/MarkovChains.html (1400 words)

	Web Site for Perfectly Random Sampling with Markov Chains:
		One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution.
		The initial states of the Markov chains are chosen at random, and if the probability of rejection in rejection sampling is known, then rigorous estimates of the mixing time are given.
		The Markov chain of interest is lifted to one that keeps track of 1) the original chain's state, and 2) the number of steps since the original chain's state took on that special value.
	dimacs.rutgers.edu /~dbwilson/exact (14686 words)

	Markov Chains (Site not responding. Last check: 2007-10-08)
		For example, a random walk on a lattice of integers returns to the initial position with probability one in one or two dimensions, but in three or more dimensions the probability of recurrence in zero.
		A Markov chain is a random process for which the future depends only on the present state; it has no memory of how the present state was reached.
		Examples of such systems abound in science, and Markov chains are a key ingredient in many mathematical models.
	www.statslab.cam.ac.uk /~grg/teaching/markovc.html (505 words)

	Markov Chains, Part 4 (Site not responding. Last check: 2007-10-08)
		A Markov (or transition) matrix is any matrix in which all entries are nonnegative and all columns sum to 1.
		In two of the examples, the Markov chain converged to the steady-state vector.
		In the third example, we saw a Markov chain that did not converge.
	www.math.duke.edu /education/ccp/materials/linalg/markov/mark4.html (202 words)

	Talk:Examples of Markov chains - Wikipedia, the free encyclopedia
		It was I who originally added the link to "Markov chain example" from Markov chain, so I claim most of the responsibility for this article being empty(ish) for so long. :-) I have finally added a worked example to the page!
		The statement above may not be true: one could construct a game in which the present move is determined not only by the present roll of the die and the current state, but also by the history of rolls of the die on previous turns.
		I also agree that "Examples of Markov chains" is a better title for the article.--Ejrh 04:14, 18 Dec 2003 (UTC)
	en.wikipedia.org /wiki/Talk:Examples_of_Markov_chains (329 words)

	Opslagstavle
		The idea is to somehow capture the overall movement of the chain, the intrinsic forces that are driving the chain towards the center of the space or away from the center.
		Note that these examples involve a somewhat atypical use of the drift criterium: the conclusion is that the random walks have no drift at all, rather than a drift towards the center or away from the center.
		In many ways the essence of the manuscript is given in example 2.29, where a straight forward and pretty mechanical proof is given of the fact that the forward recurrence time chain in a renewal setting is indeed a Markov chain.
	www.math.ku.dk /~erhansen/Markov_04 (6853 words)

	Censoring Technique in Studying Block-Structured Markov Chains (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Such Markov chains are characterized by partitioning the state space into subsets called levels, each level consisting of a number of stages.
		Examples include Markov chains of GI/M/1 type and M/G/1 type, and, more generally, Markov chains of Toeplitz type, or GI/G/1 type.
		In the analysis of such Markov chains, a number of properties and measures which relate to transitions among levels play a...
	citeseer.ist.psu.edu /464642.html (470 words)

	Markov Chains
		A Markov chain, as I understand it, is a graph that carries probabilities in its edges.
		My friend Cassidy Curtis had the great idea of generating two Markov chains from two very different sources (say from two languages) and interpolating between the two graphs, and I wrote a program in Java to do this.
		It's called "A" for historical reasons: the first Markov chain program I wrote 10 years ago was called "a" because I understood the concepts but couldn't remember the name "Markov".
	www.teamten.com /lawrence/projects/markov (1060 words)

	Lecture Summaries for 189671A, Fall 2005 (Site not responding. Last check: 2007-10-08)
		Markov Chains III: Stationary and Limit Distributions The reference for these first three lectures is 6.1-6.4 of the text.
		It includes a discussion of Conductance, Canonical paths, and their application to bound the mixing time of the Markov chain we defined on the matchings in a graph.
		Markov Chains VI: Bounding the mixing time via coupling I Here are Lecture notes for MCMC by Alisdair Sinclair.
	cgm.cs.mcgill.ca /~breed/MATH671/lects.html (280 words)

	Markov Chains (Site not responding. Last check: 2007-10-08)
		The construction of a Markov chain requires two basic ingredients, namely a transition matrix and an initial distribution.
		The first identity in (2.3), which is also called ``Markov property'', defines the ``memory'' or ``order'' of the chain.
		In this case, the chain itself is either recurrent or transient.
	crypto.mat.sbg.ac.at /~ste/diss/node6.html (979 words)

	[No title]
		In chapter 7, MMBP (Markov modulated Bernouilli process) and examples on performance analysis of ATM multiplexer, performance analysis of cache memories, slotted aloha, and architecture-based performance and reliability analysis of software are added.
		Transient Analysis of Acyclic Markov Chains, R. Marie and A. Reibman, and K. Trivedi, Performance Evaluation, Vol.
		Markov and Markov Reward Models: A Survey of Numerical Approaches, A. Reibman and R. Smith, and K. Trivedi, European Journal of Operations Research, Vol.
	www.ee.duke.edu /~kst/markov.html (824 words)

	Title page for ETD etd-61098-131249
		This thesis describes an exploratory application of a statistical analysis and modeling technique (Markov chains) for the modeling of jazz improvisation with the intended subobjective of providing increased insight into an improviser’s style and creativity through the postulation of quantitative measures of style and creativity based on the constructed Markovian analysis techniques.
		It is then explained how Markov chains and the tools for their analysis can be interpreted to determine quantitative measures of creativity and style.
		Finally, this thesis presents conclusions on Markov chain portrayals, new analysis tools and procedures, quantitative measures of creativity and style, and, in sum, that Markovian modeling is in fact a reasonable and useful modeling approach for this application.
	scholar.lib.vt.edu /theses/available/etd-61098-131249 (352 words)

	Markov Chains
		This is due to property (b) of a Markov chain.
		The most important fact that lets us model this situation as a Markov chain is that the next location for delivery depends only on the current location, not previous history.
		Try some examples to convince yourself that the vector indicating the number of people in each area after many deliveries will not change if people are moved from one state to another in the initial distribution.
	ceee.rice.edu /Books/LA/markov (2034 words)

	INFO 295 Fall 2005
		Examples of Markov chains to determine the expected number of coin flips to reach a given number of heads in a row.
		Completed Examples of Markov chains to determine the expected number of coin flips.
		Example of max probability state not on maximum probability path.
	www.cis.cornell.edu /Courses/cis295/2005fa (771 words)

	Faculty Foster (Site not responding. Last check: 2007-10-08)
		Markov chains, Transition Probability Matrices, classificaton of states, Recurrence, examples.
		Markov chains, transition probability matrices, classifacation of states.
		Continuous time markov chains, pure birth processes, poisson processes, birth and death processes, differential equations of birth and death processes.
	www.iitk.ac.in /math/files/msci_courses.html (1273 words)

	New Page 1
		A first-order Markov chain is a system where states are chosen randomly, with the probably distribution for the next state being determined only by the current state.
		In a second-order Markov chain, the probably of each state is based on the previous two states; in a third-order Markov chain, the probably of each state is based on the previous three states.
		If you try to build a third order Markov chain with just a thousand lines of text, you will get back significant passages that are exact copies from the original.
	www.cs.umd.edu /class/spring2005/cmsc132/Projects/P7/project7.html (1417 words)

	Markov Chains - Cambridge University Press
		Markov chains are central to the understanding of random processes.
		This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it.
		A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521633966 (333 words)

	Cutoff for Markov chains: some examples and applications (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: Some Markov chains converge very abruptly to their equilibrium: the total variation distance between the distribution of the chain at time t and its equilibrium measure is close to 1 until some deterministic `cutoff time', and close to 0 shortly after.
		Our goal is to introduce two families of examples of this phenomenon, focusing mainly on their possible applications.
		22 The cutoff phenomenon in finite Markov chains (context) - Diaconis - 1996
	citeseer.ist.psu.edu /401874.html (612 words)

	Topics, reading assignments, exercises (Site not responding. Last check: 2007-10-08)
		example of infinite state space transient Markov chain, properties of recurrent states.
		3/11/2003: Convergence to the stationary distribution, periodic behavior of Markov chains.
		Exercise: Prove that the queuing chain as described on page 9 of HPS is indeed a Markov chain.
	www.math.mcmaster.ca /~nediakm/S3U03/topics.html (368 words)

	Teletraffic Analysis of Telecommunications Systems (Site not responding. Last check: 2007-10-08)
		Among these, numerical treatment of structured Markov chains of M/G/1 and G/M/1 type, QBD processes, etc. are important examples.
		These Markov chains arise very naturally in the analysis of a wide variety of such systems.
		TELPACK is menu driven and contains help files and many example files to assist the user for setting up the input data files, etc. It also has the option of producing a PLOT associated with the stationary distribution of the chain.
	www.csc.fi /math_topics/Mail/NANET97-1/msg00177.html (295 words)

	Examples of Markov chains - Definition up Erdmond.Com
		A game of snakes_and_ladders or any other game whose moves are determined entirely by dice is a Markov chain.
		The columns can be labelled "sunny" and "rainy" respectively, and the rows can be labelled in the same order.
		Example of a statistical investigation of the text of "Eugene Onegin" illustrating the dependence between samples in chain
	www.erdmond.com /Examples_of_Markov_chains.html (313 words)

	Cornell Math - Laurent Saloff-Coste
		A random walk is a Markov process (g_n) on a group G where g_n is obtained from g_{n-1} by left multiplication by a random element of a fixed finite generating set of G.
		Some of the most interesting examples of such chains are connected to combinatorial problems that are not tractable by deterministic algorithms but for which a reasonable stochastic algorithm exists.
		These stochastic algorithms often involve a finite Markov chain as one of the main building blocks.
	www.math.cornell.edu /People/Faculty/saloffcoste.html (381 words)

	Electronic Journal of Probability - Vol. 7 (2002)
		Examples of Convergence and Non-convergence of Markov Chains Conditioned Not To Die
		In this paper we give two examples of evanescent Markov chains which exhibit unusual behaviour on conditioning to survive for large times.
		In the first example we show that the conditioned processes converge vaguely in the discrete topology to a limit with a finite lifetime, but converge weakly in the Martin topology to a non-Markovian limit.
	www.univie.ac.at /EMIS/journals/EJP-ECP/_ejpecp/viewarticlefe19.html?id=1302&layout=abstract (453 words)

	Prof. Martin Day - Research Page
		This produces interesting deterministic optimization problems, which can be solved explicitly in a number of (simple) examples.
		(Examples are Markov chains, queueing processes or solutions of stochastic differential equations.) The study of such stochastic processes is a branch of probability theory that has some very close connections to parts of analysis, including partial and ordinary differential equations.
		The problems of small random perturbations in particular have important connections to the calculus of variations, classical mechanics and control on nonlinear systems.
	www.math.vt.edu /people/day/research (336 words)

	Citebase - Limitations of Markov Chain Monte Carlo Algorithms for Bayesian Inference of Phylogeny
		Markov Chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference.
		In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov Chains widely used in phylogenetic inference.
		We prove that many of the popular Markov chains take exponentially long to reach their stationary distribution.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:q-bio/0505002 (733 words)

	Halfbakery: Markov Googler
		Google would then take the web pages that contain the search term and generate a page or more of Markov chains of the order specified.
		I markoved together a text dump of the first 10 Google results for "hectic" and got this mess back.
		When doing a web search for the link on the left, I found out the author of the web page wanted to apply his dadadodo to AltaVista, so this might be "prior art" for applying markov chains to search engine results.
	www.halfbakery.com /idea/Markov_20Googler (904 words)

	Metrics for Temporal Difference Learning
		Bertsekas (1995a) proposes a counterexample to the use of temporal difference methods for approximating value functions in the context of Markov chains and suggests that his results extend to the domain of Markov decision processes as well.
		In Bertsekas’ example TD(0) appeared worse than TD(1), but that is only the case when considering the 2-norm of the value function error.
		For our example, the salient information associated with a state is not the accuracy of the approximation to the value function, but the accuracy of the approximation of the difference in the values of adjacent states.
	www.leemon.com /papers/metric (2151 words)

	Publisher description for Library of Congress control number 98011959 (Site not responding. Last check: 2007-10-08)
		It is the only book currently available that combines theory and applications of computer performance evaluation with queueing networks and Markov chains, and offers an abundance of performance-evaluation algorithms, applications, and case studies.
		It examines Markov chains and solution algorithms, building on results obtained in the Markov chain chapter to derive the basic relationship for queueing networks.
		Timely and comprehensive, Queueing Networks and Markov Chains is essential for practitioners and researchers working in this rapidly evolving field, as well as for graduate students in computer science departments.
	www.loc.gov /catdir/description/wiley032/98011959.html (426 words)

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