scholarly journals Sampling Random Chordal Graphs by MCMC (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13929-13930
Author(s):  
Wenbo Sun ◽  
Ivona Bezáková
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Chordal Graph ◽  
Chordal Graphs ◽  
Random Generation ◽  
Mcmc Method ◽  
Bounded Treewidth ◽  
Graph Class ◽  
General Graphs

Chordal graphs are a widely studied graph class, with applications in several areas of computer science, including structural learning of Bayesian networks. Many problems that are hard on general graphs become solvable on chordal graphs. The random generation of instances of chordal graphs for testing these algorithms is often required. Nevertheless, there are only few known algorithms that generate random chordal graphs, and, as far as we know, none of them generate chordal graphs uniformly at random (where each chordal graph appears with equal probability). In this paper we propose a Markov chain Monte Carlo (MCMC) method to sample connected chordal graphs uniformly at random. Additionally, we propose a Markov chain that generates connected chordal graphs with a bounded treewidth uniformly at random. Bounding the treewidth parameter (which bounds the largest clique) has direct implications on the running time of various algorithms on chordal graphs. For each of the proposed Markov chains we prove that they are ergodic and therefore converge to the uniform distribution. Finally, as initial evidence that the Markov chains have the potential to mix rapidly, we prove that the chain on graphs with bounded treewidth mixes rapidly for trees (chordal graphs with treewidth bound of one).

Detection of the quality of vital signals by the Monte Carlo Markov Chain (MCMC) method and noise deleting

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Kianoush Fathi Vajargah ◽  
Sara Ghaniyari Benis ◽  
Hamid Mottaghi Golshan
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Monte Carlo Markov Chain ◽  
Mcmc Method

scholarly journals A Bayesian model for binary Markov chains

2004 ◽  
Vol 2004 (8) ◽  
pp. 421-429 ◽  
Author(s):  
Souad Assoudou ◽  
Belkheir Essebbar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Bayesian Estimation ◽  
Bayesian Model ◽  
Transition Probabilities ◽  
Simulated Data ◽  
Bayesian Estimator ◽  
Jeffreys Prior ◽  
Data Set

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

Utilizing Markov chain Monte Carlo (MCMC) method for improved glottal inverse filtering

2012 ◽  
Author(s):  
Harri Auvinen ◽  
Tuomo Raitio ◽  
Samuli Siltanen ◽  
Paavo Alku
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Inverse Filtering ◽  
Mcmc Method

Convergence Properties of Perturbed Markov Chains

1998 ◽  
Vol 35 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal ◽  
Peter O. Schwartz
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Rates Of Convergence ◽  
Geometric Ergodicity ◽  
Roundoff Error ◽  
Convergence Properties ◽  
Small Perturbations ◽  
Monte Carlo Algorithms

In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of convergence. Perturbations considered include roundoff error from computer simulation. We are motivated primarily by interest in Markov chain Monte Carlo algorithms.

scholarly journals Measuring Stellar Radial Velocity using Markov Chain Monte Carlo(MCMC) Method

2013 ◽  
Vol 9 (S298) ◽  
pp. 441-441
Author(s):  
Yihan Song ◽  
Ali Luo ◽  
Yongheng Zhao
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Distribution ◽  
Radial Velocity ◽  
Mcmc Methods ◽  
Mcmc Method ◽  
Stellar Spectra ◽  
Mcmc Simulation ◽  
Template Fitting

AbstractStellar radial velocity is estimated by using template fitting and Markov Chain Monte Carlo(MCMC) methods. This method works on the LAMOST stellar spectra. The MCMC simulation generates a probability distribution of the RV. The RV error can also computed from distribution.

scholarly journals On variance reduction for Markov chain Monte Carlo

2012 ◽  
Author(s):  
Ζωή Τσούρτη
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Markov Chains ◽  
Variance Reduction ◽  
Alternative Methods ◽  
Control Variates ◽  
Conditional Expectations ◽  
Mh Algorithm ◽  
One Step

In the present thesis we are concerned with appropriate variance reduction methods for specific classes of Markov Chain Monte Carlo (MCMC) algorithms. The variance reduction method of main interest here is that of control variates. More particularly, we focus on control variates of the form U = G − P G, for arbitrary function G, where P G stands for the one-step ahead conditional expectation, that have been proposed by Henderson (1997). A key issue for the efficient implementation of control variates is the appropriate estimation of corresponding coefficients. In the case of Markov chains, this involves the solution of Poisson equation for the function of initial interest, which in most cases is intractable. Dellaportas & Kontoyiannis (2012) have further elaborated on this issue and they have proven optimal results for the case of reversible Markov chains, avoiding that function. In this context, we concentrate on the implementation of those results for MetropolisHastings (MH) algorithm, a popular MCMC technique. In the case of MH, the main issue of concern is the assessment of one-step ahead conditional expectations, since these are not usually available in closed form expressions. The main contribution of this thesis is the development and evaluation of appropriate techniques for dealing with the use of the above type of control variates in the MH setting. The basic approach suggested is the use of Monte Carlo method for estimating one-step ahead conditional expectations as empirical means. In the case of MH this is a straightforward task requiring minimum additional analytical effort. However, it is rather computationally demanding and, hence, alternative methods are also suggested. These include importance sampling of the available data resulting from the algorithm (that is, the initially proposed or finally accepted values), additional application of the notion of control variates for the estimation of P G’s, or parallel exploitation of the values that are produced in the frame of an MH algorithm but not included in the resulting Markov chain (hybrid strategy). The ultimate purpose is the establishment of a purely efficient strategy, that is, a strategy where the variance reduction attained overcomes the additional computational cost imposed. The applicability and efficiency of the methods is illustrated through a series of diverse applications.

scholarly journals IMPLEMENTASI METODE MARKOV CHAIN MONTE CARLO DALAM PENENTUAN HARGA KONTRAK BERJANGKA KOMODITAS

2015 ◽  
Vol 4 (3) ◽  
pp. 122
Author(s):  
PUTU AMANDA SETIAWANI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Simulation Method ◽  
Commodity Price ◽  
Future Contract ◽  
Mcmc Method ◽  
Futures Contract ◽  
Mcmc Simulation ◽  
Hit And Run

The aim of the research is to implement Markov Chain Monte Carlo (MCMC) simulation method to price the futures contract of cocoa commodities. The result shows that MCMC is more flexible than Standard Monte Carlo (SMC) simulation method because MCMC method uses hit-and-run sampler algorithm to generate proposal movements that are subsequently accepted or rejected with a probability that depends on the distribution of the target that we want to be achieved. This research shows that MCMC method is suitable to be used to simulate the model of cocoa commodity price movement. The result of this research is a simulation of future contract prices for the next three months and future contract prices that must be paid at the time the contract expires. Pricing future contract by using MCMC method will produce the cheaper contract price if it compares to Standard Monte Carlo simulation.

Efficient History Matching Using the Markov-Chain Monte Carlo Method by Means of the Transformed Adaptive Stochastic Collocation Method

SPE Journal ◽  
2019 ◽  
Vol 24 (04) ◽  
pp. 1468-1489 ◽  
Author(s):  
Qinzhuo Liao ◽  
Lingzao Zeng ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Collocation Method ◽  
Posterior Distribution ◽  
History Matching ◽  
Stochastic Collocation ◽  
Mcmc Method ◽  
Stochastic Collocation Method ◽  
Surrogate System

Summary Bayesian inference provides a convenient framework for history matching and prediction. In this framework, prior knowledge, system nonlinearity, and measurement errors can be directly incorporated into the posterior distribution of the parameters. The Markov-chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior distribution. However, the MCMC method usually requires a large number of forward simulations. Hence, it can be a computationally intensive task, particularly when dealing with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model outputs in the form of polynomials using the stochastic collocation method (SCM). In addition, we use interpolation with the nested sparse grids and adaptively take into account the different importance of parameters for high-dimensional problems. Furthermore, we introduce an additional transform process to improve the accuracy of the surrogate model in case of strong nonlinearities, such as a discontinuous or unsmooth relation between the input parameters and the output responses. Once the surrogate system is built, we can evaluate the likelihood with little computational cost. Numerical results demonstrate that the proposed method can efficiently estimate the posterior statistics of input parameters and provide accurate results for history matching and prediction of the observed data with a moderate number of parameters.

scholarly journals Exact estimation for Markov chain equilibrium expectations

2014 ◽  
Vol 51 (A) ◽  
pp. 377-389 ◽  
Author(s):  
Peter W. Glynn ◽  
Chang-Han Rhee
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Monte Carlo Methods ◽  
Simulation Methods ◽  
Exact Simulation ◽  
Unbiased Estimators ◽  
Estimation Algorithms ◽  
New Class

We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue that exact estimation in the Markov chain setting provides a significant theoretical relaxation relative to exact simulation methods.

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