Efficient MCMC for Gibbs random fields using pre-computation
Efficient MCMC for Gibbs random fields using pre-computation
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DOI：
10.1214/18-ejs1504
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发表时间：
2018-01-01
影响因子：
1.1
通讯作者：
Maire, Florian
中科院分区：
文献类型：
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作者：
Boland, Aidan;Friel, Nial;Maire, Florian
吉布斯随机场（GRF）的贝叶斯推断通常被认为是一个双重棘手的问题，因为似然函数和后验分布的归一化常数都不是封闭形式的。对此类模型的后验分布的探索通常使用复杂的马尔可夫链蒙特卡罗（MCMC）方法（交换算法[28]）进行，该算法需要在每次迭代时对似然函数进行模拟。本文的目的是考虑一种方法，以显着减少这种计算开销。为此，我们介绍了一类新的算法，它使用的GRF模型，离线模拟，在指定的位置由一个网格，跨越参数空间的实现。这种策略大大加快了后验推理的速度，如几个例子所示。然而，使用预先计算的图在MCMC算法中引入了噪声，这不再是精确的。我们研究的近似MCMC算法的理论行为，并推导出收敛界使用最近的理论发展近似MCMC方法。
Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the normalizing constant of both the likelihood function and the posterior distribution are not in closed-form. The exploration of the posterior distribution of such models is typically carried out with a sophisticated Markov chain Monte Carlo (MCMC) method, the exchange algorithm [28], which requires simulations from the likelihood function at each iteration. The purpose of this paper is to consider an approach to dramatically reduce this computational overhead. To this end we introduce a novel class of algorithms which use realizations of the GRF model, simulated offline, at locations specified by a grid that spans the parameter space. This strategy speeds up dramatically the posterior inference, as illustrated on several examples. However, using the pre-computed graphs introduces a noise in the MCMC algorithm, which is no longer exact. We study the theoretical behaviour of the resulting approximate MCMC algorithm and derive convergence bounds using a recent theoretical development on approximate MCMC methods.