Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues

By John Odentrantz. Technometrics, 2000

1,771 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9db006b15116a8b5ee6398aab984a1929d5424e6

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Citations in the corpus

Plug-and-play inference for disease dynamics: measles in large and small populations as a case study (2009, background): “A Markov chain interpretation can be specified by the infinitesimal transition probabilities (Brémaud 1999)”
Sterile Neutrino Fits to Short-Baseline Neutrino Oscillation Measurements (2012, background): “Given an oscillation model, (3 + 1), (3 + 2), or (3 + 3), the corresponding independent oscillation parameters are randomly generated within their allowed range, and then varied via a Markov Chain χ2 minimization procedure [69].”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, neutral): “Later, the Cosenza group in Italy achieved some notable successes, despite the need for significant operator intervention to avoid the problem of trapping in local minima [10,11].”
Image Parsing: Unifying Segmentation, Detection, and Recognition (2003, neutral): “These two conditions ensure that p(W | I )i sthe invariant (target) probability of the Markov Chain ( Bremaud, 1999 ) in the finite space � .”
The effect of network topology on the spread of epidemics (2005, background): “This fact follows from standard theory of Markov processes with absorbing states, reviewed for instance in [4].”
Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks (2008, neutral): “Given the random walk (1) on an undirected graph, a standard way to derive a continuous-time model is to assign a continuous Poisson process of given density at each node [45], [46].”
Principles of model checking (2008, background): “Since then a variety of different aspects of Markov chains has been studied in the literature such as queuing theory [55], numerical algorithms [63, 378], reliability and performance analysis [196], and lumping [72, 237].”
Mathematical Models for Local Nontexture Inpaintings (2002, background): “As in the practice of Markov random elds [3], assign a neighborhood system to , so that each pixel 2 has its neighborhood N , a collection of \nearby" pixels (excluding itself).”
Consistency of the group Lasso and multiple kernel learning (2007, neutral): “Indeed, the condition R ( x ) dx < ¥ corresponds to a natural support condition, that is, f should be zero where X has no mass, otherwise, we will not be able to estimate f ; note the similarity with the usual condition regarding the variance of importance sampling estimation (Br´emaud, 1999).”
An Introduction to Restricted Boltzmann Machines (2012, background): “Gibbs sampler to the stationary distribution of the MRF is bounded by the following inequality (see for example [6]): |μPk − π| ≤ 1 2 |μ− π|(1− e−N ), (19)”
Limit measures for affine cellular automata II (2001, background): “μ ∈ M [ A ] is a (nonstationary) Markov random field [2, 9] with interaction range U (or “U-MRF”) if, for any W ⊂ M, and any a ∈ A, events occuring “inside” W are independent of those occuring “outside”, relative to the conditional measure μa.”