Exact-approximate sequential Monte Carlo (SMC) methods target the exact posterior of intractable likelihood models by using a non-negative unbiased estimator of the likelihood when the likelihood is computationally intractable. For state-space models, a particle filter estimator can be used to obtain an unbiased estimate of the likelihood. The efficiency of exact-approximate SMC greatly depends on the variance of the likelihood estimator, and therefore on the number of state particles used within the particle filter. We introduce a novel method to adaptively select the number of state particles within exact-approximate SMC. We also utilise the expected squared jumping distance to trigger the adaptation, and modify the exchange importance sampling method of Chopin et al. (2012) to replace the current set of state particles with the new set. The resulting algorithm is fully adaptive, and can significantly improve current methods. Code for our methods is available at https://github.com/imkebotha/adaptive-exact-approximate-smc.
翻译:近似相近的相近的蒙特卡洛(SMC)方法通过使用一个非负的、不带偏见的概率估计器,对难以计算的可能性的概率进行精确的测算。对于州空间模型,可以使用粒子过滤器测算器对概率进行公正的估计。精确的近似相近的SMC的效率在很大程度上取决于概率估测器的差异,因此取决于粒子过滤器中使用的状态粒子的数量。我们引入了一种新颖的方法,以适应性选择近似SMC中的国家粒子的数量。我们还使用预期的平方跳跃距离触发适应,并修改肖邦等人(2012年)的交换重要性取样法,以用新集取代当前粒子的状态。由此产生的算法完全适应性强,并能够大大改进当前的方法。我们方法的代码可在https://github.com/imkebotha/adptive-exact-appoint-smc查阅。