标题： Hess-MC2：使用Hessian信息和二阶提议的顺序蒙特卡洛平方 显示英文标题

标题： Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals

摘要： 在使用序贯蒙特卡罗（SMC）方法进行贝叶斯推断时，有两个考虑因素：后验近似的准确性以及计算效率。 为解决计算需求，序贯蒙特卡罗平方（SMC$^2$）非常适合高性能计算（HPC）环境。 在SMC$^2$中，提议分布的设计可以提高准确性和后验探索能力，因为较差的提议可能导致重要性权重的方差较高和粒子退化。 马尔可夫调整朗之万算法（MALA）使用梯度信息，使粒子优先探索高概率区域。 在本文中，我们通过引入二阶信息，特别是对数目标的海森矩阵，扩展了这一想法。 虽然二阶提议之前已在粒子马尔可夫链蒙特卡罗（p-MCMC）方法中被研究过，但我们在SMC$^2$框架中首次引入了它们。 二阶提议不仅使用梯度（一阶导数），还使用目标分布的曲率（二阶导数）。 在合成模型上的实验结果表明，与其它提议相比，我们的方法在步长选择和后验近似准确性方面具有优势。 显示英文摘要

摘要： When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo Squared (SMC$^2$) is well-suited for high-performance computing (HPC) environments. The design of the proposal distribution within SMC$^2$ can improve accuracy and exploration of the posterior as poor proposals may lead to high variance in importance weights and particle degeneracy. The Metropolis-Adjusted Langevin Algorithm (MALA) uses gradient information so that particles preferentially explore regions of higher probability. In this paper, we extend this idea by incorporating second-order information, specifically the Hessian of the log-target. While second-order proposals have been explored previously in particle Markov Chain Monte Carlo (p-MCMC) methods, we are the first to introduce them within the SMC$^2$ framework. Second-order proposals not only use the gradient (first-order derivative), but also the curvature (second-order derivative) of the target distribution. Experimental results on synthetic models highlight the benefits of our approach in terms of step-size selection and posterior approximation accuracy when compared to other proposals.