论文标题
关于交换算法的理论特性
On the Theoretical Properties of the Exchange Algorithm
论文作者
论文摘要
Exchange算法是大都市最流行的扩展之一 - 悬挂算法，可从双重截止分布中进行样品。但是，交换算法的理论探索非常有限。例如，诸如“交换算法会以几何速率汇聚？”之类的自然问题？或“交换算法是否接受中心限制定理？”尚未回答。在本文中，我们根据渐近方差和收敛速度研究了交换算法的理论特性。我们将交换算法与原始大都市（Hastings算法）进行了比较，并为交换算法的几何形象提供了必要和足够的条件。此外，我们证明我们的结果可以应用于各种实际应用，例如位置模型，高斯模型，泊松模型和大量的指数家庭，其中包括交换算法的大多数实际应用。还建立了交换算法的中心限制定理。我们的结果证明了交换算法的理论实用性是合理的。
The exchange algorithm is one of the most popular extensions of the Metropolis--Hastings algorithm to sample from doubly-intractable distributions. However, the theoretical exploration of the exchange algorithm is very limited. For example, natural questions like `Does exchange algorithm converge at a geometric rate?' or `Does the exchange algorithm admit a Central Limit Theorem?' have not been answered yet. In this paper, we study the theoretical properties of the exchange algorithm, in terms of asymptotic variance and convergence speed. We compare the exchange algorithm with the original Metropolis--Hastings algorithm and provide both necessary and sufficient conditions for the geometric ergodicity of the exchange algorithm. Moreover, we prove that our results can be applied to various practical applications such as location models, Gaussian models, Poisson models, and a large class of exponential families, which includes most of the practical applications of the exchange algorithm. A central limit theorem for the exchange algorithm is also established. Our results justify the theoretical usefulness of the exchange algorithm.
