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1,281
Improved bounds for mixing rates of Markov chains and multicommodity flow
 Combinatorics, Probability and Computing
, 1992
"... The paper is concerned with tools for the quantitative analysis of finite Markov chains whose states are combinatorial structures. Chains of this kind have algorithmic applications in many areas, including random sampling, approximate counting, statistical physics and combinatorial optimisation. The ..."
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Cited by 205 (8 self)
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. The efficiency of the resulting algorithms depends crucially on the mixing rate of the chain, i.e., the time taken for it to reach its stationary or equilibrium distribution. The paper presents a new upper bound on the mixing rate, based on the solution to a multicommodity flow problem in the Markov chain
A Hidden Markov Model approach to variation among sites in rate of evolution.
 Mol Biol Evol
, 1996
"... Abstract The method of hidden Markov models is used to allow for unequal and unknown evolutionary rates at different sites in molecular sequences. Rates of evolution at different sites are assumed to be drawn from a set of possible rates, with a finite number of possibilities. The overall likelihoo ..."
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Cited by 244 (1 self)
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likelihood of a phylogeny is calculated as a sum of terms, each term being the probability of the data given a particular assignment of rates to sites, times the prior probability of that particular combination of rates. The probabilities of different rate combinations are specified by a stationary Markov
Being Bayesian about network structure
 Machine Learning
, 2000
"... Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model sel ..."
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Cited by 299 (3 self)
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the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders
Measurement and modeling of the temporal dependence in packet loss
, 1999
"... Abstract — Understanding and modelling packet loss in the Internet is especially relevant for the design and analysis of delaysensitive multimedia applications. In this paper, we present analysis of ¢¡¤ £ hours of endtoend unicast and multicast packet loss measurement. From these we selected ¥§ ¦ ..."
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Cited by 270 (11 self)
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of three models of increasing complexity: the Bernoulli model, the 2state Markov chain model and � theth order Markov chain model. Out of � £ the trace segments considered, the Bernoulli model was found to be accurate for ¥ segments, the 2state model was found to be accurate for ¢ ¨ segments. A Markov
On adaptive markov chain monte carlo algorithm
 BERNOULLI
, 2005
"... We look at adaptive MCMC algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the past of the process. We show under certain conditions that the generated stochastic process is ergodic, with appropriate stationar ..."
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Cited by 122 (29 self)
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stationary distribution. We then consider the Random Walk Metropolis (RWM) algorithm with normal proposal and scale parameter σ. We propose an adaptive version of this algorithm that sequentially adjusts σ using a RobbinsMonro type algorithm in order to nd the optimal scale parameter σopt as in Roberts et
Markov Chain Monte Carlo Simulation Methods in Econometrics
, 1993
"... We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literat ..."
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Cited by 153 (9 self)
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We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical
Stationary Analysis of Markov Chains
, 2004
"... Markov Chains (Under the direction of William J. Stewart). With existing numerical methods, the computation of stationary distributions for large Markov chains is still timeconsuming, a direct result of the state explosion problem. In this thesis, we introduce a rank reduction method for computing ..."
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Markov Chains (Under the direction of William J. Stewart). With existing numerical methods, the computation of stationary distributions for large Markov chains is still timeconsuming, a direct result of the state explosion problem. In this thesis, we introduce a rank reduction method for computing
Bayesian inference on phylogeny and its impact on evolutionary biology.
 Science
, 2001
"... 1 As a discipline, phylogenetics is becoming transformed by a flood of molecular data. These data allow broad questions to be asked about the history of life, but also present difficult statistical and computational problems. Bayesian inference of phylogeny brings a new perspective to a number of o ..."
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Cited by 235 (10 self)
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)]. MCMC has revolutionized Bayesian inference, with recent applications to Bayesian phylogenetic inference (13) as well as many other problems in evolutionary biology (57). The basic idea is to construct a Markov chain that has as its state space the parameters of the statistical model and a stationary
Equilibrium in a Dynamic Limit Order Market
, 2004
"... We model a dynamic limit order market as a stochastic sequential game. Since the model is analytically intractable, we provide an algorithm based on Pakes and McGuire (2001) to find a stationary Markovperfect equilibrium. Given the stationary equilibrium, we generate artificial time series and p ..."
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Cited by 209 (10 self)
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We model a dynamic limit order market as a stochastic sequential game. Since the model is analytically intractable, we provide an algorithm based on Pakes and McGuire (2001) to find a stationary Markovperfect equilibrium. Given the stationary equilibrium, we generate artificial time series
The computation of stationary distributions of Markov chains through perturbations
 J. Appl. Math. Stoch. Anal
, 1991
"... An algorithmic procedure for the determination of the stationary distribution of a finite, mstate, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations of the ..."
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Cited by 1 (0 self)
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An algorithmic procedure for the determination of the stationary distribution of a finite, mstate, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations
Results 11  20
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