Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions
Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions
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DOI：
10.1239/aap/1396360114
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发表时间：
2014-03
影响因子：
1.2
通讯作者：
A. Beskos;D. Crisan;A. Jasra;N. Whiteley
中科院分区：
文献类型：
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作者：
A. Beskos;D. Crisan;A. Jasra;N. Whiteley
在本文中，我们开发了一系列与序列蒙特卡罗（SMC）采样器算法分析相关的结果，在高维独立和同分布的目标概率的背景下。SMC采样器算法可以设计为从单个概率分布中采样，使用蒙特卡罗近似期望。给定d维的目标密度，我们的结果与d→∞有关，而蒙特卡罗样本的数量N保持固定。我们推导了使用SMC采样器得到的估计的蒙特卡罗误差的显式界和与目标相关的归一化常数估计的精确渐近相对误差。建立了混沌算法的边缘传播特性。这些结果是当算法的代价为0 （Nd）时推导出来的。
In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. The SMC samplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density in d dimensions our results are concerned with d → ∞, while the number of Monte Carlo samples, N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative -error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd 2).