一种用于多元混合分布非参数估计的PRticle滤波算法
A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions
AI总结：
针对PR算法在高维混合分布估计中计算归一化常数效率低的问题，提出PRticle滤波算法，通过自适应重权粒子集实现蒙特卡罗近似，经理论与实验验证了其收敛性与准确性。
摘要：
预测递归（PR）是一种快速的递归算法，可在通用混合模型下对混合分布给出平滑估计。然而，PR算法每次迭代都需要计算归一化常数。当混合分布的支撑集维度相对较低时，这不成问题，因为可使用求积法且效率很高。但当支撑集维度较高时，求积法效率低下，且没有明显的基于蒙特卡罗的替代方法。本文提出一种新策略，称为PRticle滤波算法，通过添加滤波机制增强基本PR算法，该机制沿更新序列自适应地对初始粒子集重新加权，以获得归一化常数的蒙特卡罗近似。本文建立了PRticle滤波近似的收敛性质，并通过模拟研究和标记空间点过程数据分析验证了其经验准确性。
英文摘要：
Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration. When the support of the mixing distribution is of relatively low dimension, this is not a problem since quadrature methods can be used and are very efficient. But when the support is of higher dimension, quadrature methods are inefficient and there is no obvious Monte Carlo-based alternative. In this paper, we propose a new strategy, which we refer to as a PRticle filter, wherein we augment the basic PR algorithm with a filtering mechanism that adaptively reweights an initial set of particles along the updating sequence which are used to obtain Monte Carlo approximations of the normalizing constants. Convergence properties of the PRticle filter approximation are established and its empirical accuracy is demonstrated with simulation studies and a marked spatial point process data analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
