Sequential Monte Carlo squared (SMC\(^2\)) methods can be used for parameter inference of intractable likelihood state-space models. These methods replace the likelihood with an unbiased particle filter estimate, similarly to particle Markov chain Monte Carlo (MCMC). As with particle MCMC, the efficiency of SMC\(^2\) greatly depends on the variance of the likelihood estimator, and therefore on the number of state particles used within the particle filter. We introduce novel methods to adaptively select the number of state particles within SMC\(^2\) using the expected squared jumping distance to trigger the adaptation, and modifying the exchange importance sampling method of Chopin et al. (J R Stat Soc: Ser B (Stat Method) 75(3):397–426, 2012) to replace the current set of state particles with the new set of state particles. The resulting algorithm is fully automatic, and can significantly improve current methods. Code for our methods is available at https://github.com/imkebotha/adaptive-exact-approximate-smc.

顺序蒙特卡洛平方 (SMC \(^2\) ) 方法可用于难以处理的似然状态空间模型的参数推断。这些方法用无偏粒子滤波器估计代替似然，类似于粒子马尔可夫链蒙特卡罗 (MCMC)。与粒子 MCMC 一样，SMC \(^2\)的效率在很大程度上取决于似然估计的方差，因此取决于粒子滤波器中使用的状态粒子的数量。我们引入了新的方法来自适应地选择 SMC \(^2\)中的状态粒子数使用期望的平方跳跃距离来触发适应，并修改 Chopin 等人的交换重要性采样方法。(JR Stat Soc: Ser B (Stat Method) 75(3):397–426, 2012) 用新的状态粒子集替换当前的状态粒子集。由此产生的算法是全自动的，可以显着改进当前的方法。我们方法的代码可在 https://github.com/imkebotha/adaptive-exact-approximate-smc 获得。