We consider the problem of designing efficient particle filters for twisted Feynman--Kac models. Particle filters using twisted models can deliver low error approximations of statistical quantities and such twisting functions can be learnt iteratively. Practical implementations of these algorithms are complicated by the need to (i) sample from the twisted transition dynamics, and (ii) calculate the twisted potential functions. We expand the class of applicable models using rejection sampling for (i) and unbiased approximations for (ii) using a random weight particle filter. We characterise the average acceptance rates within the particle filter in order to control the computational cost, and analyse the asymptotic variance. Empirical results show the mean squared error of the normalising constant estimate in our method is smaller than a memory-equivalent particle filter but not a computation-equivalent filter. Both comparisons are improved when more efficient sampling is possible which we demonstrate on a stochastic volatility model.
翻译:我们考虑了为扭曲的Feynman-Kac模型设计高效粒子过滤器的问题。使用扭曲模型的粒子过滤器可以提供低误差的统计数量近似值,这种扭曲功能可以反复学习。这些算法的实际实施由于需要(一) 从扭曲的过渡动态中抽样,以及(二) 计算扭曲的潜在功能而变得复杂。我们使用(一) 的拒绝抽样和(二) 使用随机重量粒子过滤器的不偏倚近度来扩大适用模型的类别。我们用随机重量粒子过滤器来描述粒子过滤器中的平均接受率,以便控制计算成本,并分析无干扰差异。 Empical结果显示,我们方法中正常的常数估计的平均平方错误小于一个内存等粒子过滤器,而不是一个计算等值过滤器。如果能够进行更有效的取样,我们用一个随机波动模型来演示,那么两种比较都会改进。