Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation for the first and second derivatives of the log likelihood via simulation-based sequential Monte Carlo smoothing and proved that the approximation has some attractive theoretical properties. We investigated an iterated smoothing algorithm carrying out likelihood maximization using these derivative approximations. Further, we developed a new iterated smoothing algorithm, using a modification of these derivative estimates, for which we establish both theoretical results and effective practical performance. On benchmark computational challenges, this method beat the first-order iterated filtering algorithm. The method’s performance was comparable to a recently developed iterated filtering algorithm based on an iterated Bayes map. Our iterated smoothing algorithm and its theoretical justification provide new directions for future developments in simulation-based inference for latent variable models such as partially observed Markov process models.

中文翻译：

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二阶迭代平滑算法。

由于在许多实际情况下不可能直接计算似然性，因此基于模拟的部分观测随机动态模型推理目前正受到广泛关注。迭代滤波方法可使用基于仿真的顺序蒙特卡洛滤波器来实现似然函数的最大化。Doucet等。（2013年）通过基于模拟的顺序蒙特卡洛平滑开发了对数似然的一阶和二阶导数的近似值，并证明了该近似值具有一些吸引人的理论特性。我们研究了使用这些导数逼近进行似然最大化的迭代平滑算法。此外，我们通过修改这些导数估算值，开发了一种新的迭代平滑算法，为此，我们建立了理论结果和有效的实际表现。在基准计算挑战中，此方法优于一阶迭代过滤算法。该方法的性能与最近开发的基于迭代贝叶斯图的迭代过滤算法相当。我们的迭代平滑算法及其理论依据为潜变量模型（例如部分观测到的马尔可夫过程模型）的基于仿真的推理提供了未来发展的新方向。