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

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.

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Robustness analysis of underground powerhouse construction simulation based on Markov Chain Monte Carlo method

Science China Technological Sciences ◽

10.1007/s11431-015-5859-3 ◽

2015 ◽

Vol 59 (2) ◽

pp. 252-264 ◽

Cited By ~ 6

Author(s):

DengHua Zhong ◽

Lei Bi ◽

Jia Yu ◽

MengQi Zhao

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Monte Carlo Method ◽

Robustness Analysis ◽

Construction Simulation ◽

Underground Powerhouse ◽

Simulation Based

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River water quality modelling and simulation based on Markov Chain Monte Carlo computation and Bayesian inference model

African Journal of Science Technology Innovation and Development ◽

10.1080/20421338.2019.1692460 ◽

2020 ◽

Vol 12 (6) ◽

pp. 771-785 ◽

Cited By ~ 1

Author(s):

Mrunmayee Manjari Sahoo ◽

Kanhu Charan Patra

Keyword(s):

Water Quality ◽

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Bayesian Inference ◽

Water Quality Modelling ◽

Inference Model ◽

Monte Carlo Computation ◽

Simulation Based ◽

River Water Quality Modelling

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Tight reservoir oiliness numerical simulation based on a Markov chain Monte Carlo (MCMC) method: A case study of the upper Triassic Yanchang-6 formation (T3ch6 Fm.) outcrop of Ordos Basin

Journal of Petroleum Science and Engineering ◽

10.1016/j.petrol.2019.01.010 ◽

2019 ◽

Vol 175 ◽

pp. 1150-1159 ◽

Cited By ~ 1

Author(s):

Yaohua Li ◽

Yan Song ◽

Shu Jiang ◽

Zhenxue Jiang ◽

Wei Yang ◽

...

Keyword(s):

Numerical Simulation ◽

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Ordos Basin ◽

Upper Triassic ◽

Mcmc Method ◽

Tight Reservoir ◽

Simulation Based

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Optimized Markov Chain Monte Carlo for Signal Detection in MIMO Systems: An Analysis of the Stationary Distribution and Mixing Time

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2014.2334558 ◽

2014 ◽

Vol 62 (17) ◽

pp. 4436-4450 ◽

Cited By ~ 15

Author(s):

Babak Hassibi ◽

Morten Hansen ◽

Alexandros G. Dimakis ◽

Haider Ali Jasim Alshamary ◽

Weiyu Xu

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Signal Detection ◽

Stationary Distribution ◽

Mimo Systems ◽

Mixing Time

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Exact Markov Chain Monte Carlo Algorithms and Their Applications in Probabilistic Data Analysis and Inference

Intelligent Data Analysis ◽

10.4018/978-1-59904-982-3.ch010 ◽

2009 ◽

pp. 161-183

Author(s):

Dominic Savio Lee

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Data Analysis ◽

Markov Chain Monte Carlo ◽

Markov Chains ◽

Stationary Distribution ◽

Probabilistic Data ◽

Perfect Sampling ◽

Monte Carlo Algorithms ◽

Sampling Algorithms

This chapter describes algorithms that use Markov chains for generating exact sample values from complex distributions, and discusses their use in probabilistic data analysis and inference. Its purpose is to disseminate these ideas more widely so that their use will become more widespread, thereby improving Monte Carlo simulation results and stimulating greater research interest in the algorithms themselves. The chapter begins by introducing Markov chain Monte Carlo (MCMC), which stems from the idea that sample values from a desired distribution f can be obtained from the stationary states of an ergodic Markov chain whose stationary distribution is f. To get sample values that have distribution f exactly, it is necessary to detect when the Markov chain has reached its stationary distribution. Under certain conditions, this can be achieved by means of coupled Markov chains—these conditions and the resulting exact MCMC or perfect sampling algorithms and their applications are described.

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Widening and clustering techniques allowing the use of monotone CFTP algorithm

Monte Carlo Methods and Applications ◽

10.1515/mcma-2015-0111 ◽

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.

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