Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo

Bouranis Lampros; Friel Nial; Maire Florian

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Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo

机译：使用嘈杂可逆跳转Markov Chain Monte Carlo模型比较吉布斯随机字段

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The reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying dimensions. A naive implementation of RJMCMC to models like Gibbs random fields suffers from computational difficulties: the posterior distribution for each model is termed doubly-intractable since computation of the likelihood function is rarely available. Consequently, it is simply impossible to simulate a transition of the Markov chain in the presence of likelihood intractability. A variant of RJMCMC is presented, called noisy RJMCMC, where the underlying transition kernel is replaced with an approximation based on unbiased estimators. Based on previous theoretical developments, convergence guarantees for the noisy RJMCMC algorithm are provided. The experiments show that the noisy RJMCMC algorithm can be much more efficient than other exact methods, provided that an estimator with controlled Monte Carlo variance is used, a fact which is in agreement with the theoretical analysis. (C) 2018 Elsevier B.V. All rights reserved.

机译：可逆跳转马尔可夫链蒙特卡罗（RJMCMC）方法通过探索由多种可能变化尺寸的多种型号组成的采样空间，为贝叶斯估计和模型比较提供了跨模型仿真方法。刚刚实现GIBBS随机字段等模型的天真地实现了计算困难：每个模型的后部分布被称为双重侵扰，因为似然函数很少可用。因此，在存在似然性难善存在下，根本无法模拟马尔可夫链的转变。 rjmcmc的变体被呈现，称为噪声rjmcmc，其中基于非偏见的估计器的近似替换底层转换内核。基于先前的理论发展，提供了嘈杂的RJMCMC算法的收敛保证。实验表明，如果使用具有受控的蒙特卡罗方差的估计，则噪声RJMCMC算法可以比其他确切方法更有效，这是一个与理论分析一致的事实。（c）2018 Elsevier B.v.保留所有权利。

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来源
《Computational statistics & data analysis》 |2018年第2018期|共21页
作者
Bouranis Lampros; Friel Nial; Maire Florian;
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作者单位

Univ Coll Dublin Sch Math &

Stat Dublin Ireland;

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原文格式 PDF
正文语种 eng
中图分类概率论与数理统计;数据处理、数据处理系统;
关键词
Bayes factors; Intractable likelihoods; Markov random fields; Noisy MCMC;

机译：贝叶斯因素;顽固的可能性;马尔可夫随机字段;嘈杂的MCMC;

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专利

1. Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo [J] . Bouranis Lampros, Friel Nial, Maire Florian Computational statistics & data analysis . 2018,第期

机译：使用嘈杂可逆跳转Markov Chain Monte Carlo模型比较吉布斯随机字段
2. Model selection in finite mixture of regression models: a Bayesian approach with innovative weighted g priors and reversible jump Markov chain Monte Carlo implementation [J] . Liu Wei, Zhang Bo, Zhang Zhiwei, Journal of statistical computation and simulation . 2015,第10a12期

机译：回归模型的有限混合中的模型选择：具有创新加权g先验和可逆跳跃马尔可夫链蒙特卡洛实现的贝叶斯方法
3. Comparison of reversible-jump Markov-chain-Monte-Carlo learning approach with other methods for missing enzyme identification. [J] . Geng B, Zhou X, Zhu J, Journal of biomedical informatics. . 2008,第2期

机译：可逆跳跃马尔可夫链蒙特卡洛学习方法与其他方法的遗漏酶鉴定的比较。
4. Multisite updating Markov chain Monte Carlo algorithm for morphologically constrained Gibbs random fields [C] . Krishnamoorthy Sivakumar, Texas AM Univ., College Station, Bayesian Inference for Inverse Problems . 1998

机译：形态约束吉布斯随机场的多站点更新马尔可夫链蒙特卡罗算法
5. Detecting piecewise linear networks using reversible jump Markov Chain Monte Carlo. [D] . Apte, Akshay. 2010

机译：使用可逆跳跃马尔可夫链蒙特卡罗检测分段线性网络。
6. Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo [O] . Mark Pagel, Andrew Meade 2008

机译：用可逆跳跃马尔可夫链蒙特卡洛法对系统发育推断中的异质性进行建模
7. Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo [O] . Bouranis, Lampros, Friel, Nial, Maire, Florian 2017

机译：使用噪声可逆跳跃的Gibbs随机场模型比较马尔可夫链蒙特卡洛

Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo

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