Norges Teknisk-naturvitenskapelige Universitet Antithetic Coupling of Two Gibbs Sampler Chains Antithetic Coupling of Two Gibbs Sampler Chains
Norges Teknisk-naturvitenskapelige Universitet Antithetic Coupling of Two Gibbs Sampler Chains Antithetic Coupling of Two Gibbs Sampler Chains
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Norges Teknisk-naturvitenskapelige Universitet 两个 Gibbs 采样器链的对偶耦合 两个 Gibbs 采样器链的对偶耦合
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通讯作者：
H. Rue
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作者：
A. Frigessi;J. Gåsemyr;H. Rue;H. Rue
摘要 两个耦合的吉布斯采样器链都具有不变的概率密度 ，以链负相关的方式并行运行。这使我们能够定义期望 E(f (X)) 的渐近无偏估计量，相对于通常的吉布斯采样器，以可比的计算成本实现显着的方差减少。我们表明，如果 是有吸引力的且 f 在 X 的所有分量中单调非递减，则基于新算法的估计量的方差始终小于单个吉布斯采样器链的方差。对于非吸引力目标 ，我们的结果并不完整：当 是多元正态密度或 Ising 模型时，新的反题算法比标准吉布斯采样器好一个数量级。更一般地说，非严格的论证和数值实验支持对偶耦合吉布斯采样器对于其他非吸引力模型的有用性。在我们的实验中，方差最多减少到三分之一，效率也显着提高。
SUMMARY Two coupled Gibbs sampler chains, both with invariant probability density , are run in parallel in such a way that the chains are negatively correlated. This allows us to define an asymp-totically unbiased estimator of the expectation E(f (X)) with respect to which achieves significant variance reduction with respect to the usual Gibbs sampler at comparable computational cost. We show that the variance of the estimator based on the new algorithm is always smaller than the variance of a single Gibbs sampler chain, if is attractive and f is monotone non-decreasing in all components of X. For non-attractive targets , our results are not complete: The new anti-thetic algorithm outperforms the standard Gibbs sampler by one order of magnitude when is a multivariate normal density or the Ising model. More generally, non-rigorous arguments and numerical experiments support the usefulness of the antithetically coupled Gibbs samplers also for other non-attractive models. In our experiments the variance is reduced to at most a third and the efficiency also improves significantly.