This paper investigates a family of adaptive importance sampling algorithms for probability density function exploration. The proposed approach consists in modeling the sampling policy, the sequence of distributions used to generate the particles, as a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a naive heavy tail density. When the share of samples generated according to the naive density goes to zero but not too quickly, two types of results are established: (i) uniform convergence rates are derived for the sampling policy estimate; (ii) a central limit theorem is obtained for the sampling policy estimate as well as for the resulting integral estimates. The fact that the asymptotic variance is the same as the variance of an oracle procedure, in which the sampling policy is chosen as the optimal one, illustrates the benefits of the approach. The practical behavior of the resulting algorithms is illustrated in a simulation study.
翻译:本文调查了一组用于概率密度功能勘探的适应性重要抽样算法。拟议方法包括模拟取样政策、用于产生粒子的分布序列,作为灵活内核密度估计(基于先前的粒子)和天真的重尾密度之间的混合分布。当根据天真密度生成的样本比例降至零但不会太快时,可以确定两类结果:(一)为取样政策估计得出统一的趋同率;(二)为取样政策估计和由此产生的综合估计得出一个中心限值。在抽样政策选择为最佳的甲骨文程序上,非抽取差异与甲骨骼程序的差异相同,这表明了该方法的好处。模拟研究中说明了由此得出的算法的实际行为。