Poisson approximate likelihood compared to the particle filter

Yize Hao, Aaron A. Abkemeier, Edward L. Ionides
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Abstract

Filtering algorithms are fundamental for inference on partially observed stochastic dynamic systems, since they provide access to the likelihood function and hence enable likelihood-based or Bayesian inference. A novel Poisson approximate likelihood (PAL) filter was introduced by Whitehouse et al. (2023). PAL employs a Poisson approximation to conditional densities, offering a fast approximation to the likelihood function for a certain subset of partially observed Markov process models. A central piece of evidence for PAL is the comparison in Table 1 of Whitehouse et al. (2023), which claims a large improvement for PAL over a standard particle filter algorithm. This evidence, based on a model and data from a previous scientific study by Stocks et al. (2020), might suggest that researchers confronted with similar models should use PAL rather than particle filter methods. Taken at face value, this evidence also reduces the credibility of Stocks et al. (2020) by indicating a shortcoming with the numerical methods that they used. However, we show that the comparison of log-likelihood values made by Whitehouse et al. (2023) is flawed because their PAL calculations were carried out using a dataset scaled differently from the previous study. If PAL and the particle filter are applied to the same data, the advantage claimed for PAL disappears. On simulations where the model is correctly specified, the particle filter outperforms PAL.
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泊松近似似然与粒子滤波的比较
滤波算法是部分观测随机动态系统推断的基础,因为它们提供了对似然函数的访问,从而实现基于似然或贝叶斯的推断。怀特豪斯等人(2023 年)提出了一种新型泊松近似似然(PAL)滤波器。PAL 对条件密度采用泊松近似,为部分观测的马尔可夫过程模型的某些子集提供了快速近似似然函数。怀特豪斯等人(2023 年)在表 1 中对 PAL 进行了比较,认为 PAL 比标准粒子滤波算法有很大改进。这一证据基于 Stocks 等人(2020 年)以前的一项科学研究中的模型和数据,可能表明研究人员在面对类似模型时应使用 PAL 而不是粒子滤波方法。从表面价值来看,这一证据也降低了斯托克斯等人(2020 年)的可信度,因为它表明他们使用的数值方法存在缺陷。然而,我们发现怀特豪斯等人(2023 年)的对数似然值比较存在缺陷,因为他们的 PAL 计算使用的数据集比例与前一项研究不同。如果将 PAL 和粒子过滤器应用于相同的数据,那么 PAL 的优势就会消失。在正确指定模型的模拟中,粒子滤波器的性能优于 PAL。
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