Results 181 to 190 of about 1,572 (217)
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2005
Abstract Useful models of the real world have to satisfy two conflicting requirements: they must be sufficiently complicated to describe complex systems, but they must also be sufficiently simple for us to analyse them. This chapter introduces Markov chains, which have successfully modelled a huge range of scientific and social phenomena,
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Abstract Useful models of the real world have to satisfy two conflicting requirements: they must be sufficiently complicated to describe complex systems, but they must also be sufficiently simple for us to analyse them. This chapter introduces Markov chains, which have successfully modelled a huge range of scientific and social phenomena,
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IEEE Trans. Inf. Theory, 1984
Summary: The Markov chain that has maximum entropy for given first and second moments is determined. The solution provides a discrete analog to the continuous Gauss-Markov process.
Jørn Justesen, Tom Høholdt
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Summary: The Markov chain that has maximum entropy for given first and second moments is determined. The solution provides a discrete analog to the continuous Gauss-Markov process.
Jørn Justesen, Tom Høholdt
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1997
Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov ...
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Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov ...
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2006
Motivated by the computational difficulty of analyzing very large Markov chains, we define a notion of clusters in (not necessarily reversible) Markov chains, and explore the possibility of analyzing a cluster “in vitro,” without regard to the remainder of the chain.
Nir Ailon, Steve Chien, Cynthia Dwork
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Motivated by the computational difficulty of analyzing very large Markov chains, we define a notion of clusters in (not necessarily reversible) Markov chains, and explore the possibility of analyzing a cluster “in vitro,” without regard to the remainder of the chain.
Nir Ailon, Steve Chien, Cynthia Dwork
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Factorization of Markov Chains
Journal of Theoretical Probability, 2004Let \(A\) be a (sub)stochastic \(d\times d\) matrix, with \(d=\infty\) possible. Existence of a factorization \(I-A=(I-B)(I-C)\) is proved for matrices \(B\) and \(C\) which are in particular triangular. The purpose is to solve in two steps equations \((I-A)x=g\) by recurrence. The author's paper [Sb. Math. 189, No.
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The Markov chain of colourings
1995The Markov chain of good (proper) colourings of an n-vertex graph starts with an n-colouring and converges to a uniform distribution over all proper colourings with at most n colours. We study theoretically and experimentally the behaviour of this chain and concentrate in particular on a quantity μ which is the mean number of colours used in the ...
J. Eric Bartels, Dominic Welsh
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IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003
We propose a model called a pairwise Markov chain (PMC), which generalizes the classical hidden Markov chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process.
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We propose a model called a pairwise Markov chain (PMC), which generalizes the classical hidden Markov chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process.
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Theory of Probability & Its Applications, 1961
This paper discusses some new results related to ergodic and limit theorems and also to the repeated logarithm low for inhomogeneous Markov chains. Theorems are formulated and proved for conditions that were not treated in the literature; some estimates obtained previously by S. N. Bernshtein are employed.Lemma 1 is of greatest importance in the paper.
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This paper discusses some new results related to ergodic and limit theorems and also to the repeated logarithm low for inhomogeneous Markov chains. Theorems are formulated and proved for conditions that were not treated in the literature; some estimates obtained previously by S. N. Bernshtein are employed.Lemma 1 is of greatest importance in the paper.
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Annals of Mathematics and Artificial Intelligence, 2014
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