Widening and clustering techniques allowing the use of monotone CFTP algorithm

2015 ◽  
Vol 21 (4) ◽  
Author(s):  
Mohamed Yasser Bounnite ◽  
Abdelaziz Nasroallah
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Simulations ◽  
State Space ◽  
Stationary Distribution ◽  
Clustering Techniques ◽  
Clustering Technique ◽  
The Past ◽  
Coupling From The Past

AbstractThe standard Coupling From The Past (CFTP) algorithm is an interesting tool to sample from exact stationary distribution of a Markov chain. But it is very expensive in time consuming for large chains. There is a monotone version of CFTP, called MCFTP, that is less time consuming for monotone chains. In this work, we propose two techniques to get monotone chain allowing use of MCFTP: widening technique based on adding two fictitious states and clustering technique based on partitioning the state space in clusters. Usefulness and efficiency of our approaches are showed through a sample of Markov Chain Monte Carlo simulations.

scholarly journals Generating a Random Sink-free Orientation in Quadratic Time

10.37236/1627 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
Henry Cohn ◽  
Robin Pemantle ◽  
James Propp
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Undirected Graph ◽  
Randomized Algorithm ◽  
Degree Of Approximation ◽  
The Past ◽  
Coupling From The Past ◽  
Mean Time ◽  
Random Sink

A sink-free orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to sample approximately from the uniform distribution on sink-free orientations in time $O(m^3 \log (1 / \varepsilon))$, where $m$ is the number of edges and $\varepsilon$ the degree of approximation. Huber (1998) uses coupling from the past to obtain an exact sample in time $O(m^4)$. We present a simple randomized algorithm inspired by Wilson's cycle popping method which obtains an exact sample in mean time at most $O(nm)$, where $n$ is the number of vertices.

scholarly journals Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions

2015 ◽  
Vol 14 (4) ◽  
Author(s):  
Patrick Muchmore ◽  
Paul Marjoram
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stationary Distribution ◽  
Large Family ◽  
Multivariate Normal ◽  
Elliptically Contoured Distributions ◽  
Simulation Based ◽  
A Chain ◽  
Elliptically Contoured

AbstractRecent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible.

Lifetime PCB 153 bioaccumulation and pharmacokinetics in pilot whales: Bayesian population PBPK modeling and Markov chain Monte Carlo simulations

Chemosphere ◽  
2014 ◽  
Vol 94 ◽  
pp. 91-96 ◽  
Author(s):  
Liesbeth Weijs ◽  
Anthony C. Roach ◽  
Raymond S.H. Yang ◽  
Robin McDougall ◽  
Michael Lyons ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Simulations ◽  
Pbpk Modeling ◽  
Pilot Whales

A kind of dual form for coupling from the past algorithm, to sample from Markov chain steady-state probability

2019 ◽  
Vol 25 (4) ◽  
pp. 317-327
Author(s):  
Abdelaziz Nasroallah ◽  
Mohamed Yasser Bounnite
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Steady State ◽  
Performance Comparison ◽  
State Probability ◽  
Steady State Probability ◽  
Dual Form ◽  
The Past ◽  
Coupling From The Past ◽  
History Of

Abstract The standard coupling from the past (CFTP) algorithm is an interesting tool to sample from exact Markov chain steady-state probability. The CFTP detects, with probability one, the end of the transient phase (called burn-in period) of the chain and consequently the beginning of its stationary phase. For large and/or stiff Markov chains, the burn-in period is expensive in time consumption. In this work, we propose a kind of dual form for CFTP called D-CFTP that, in many situations, reduces the Monte Carlo simulation time and does not need to store the history of the used random numbers from one iteration to another. A performance comparison of CFTP and D-CFTP will be discussed, and some numerical Monte Carlo simulations are carried out to show the smooth running of the proposed D-CFTP.

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