{"ID":2895978,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.07461","arxiv_id":"2507.07461","title":"Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals","abstract":"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.","short_abstract":"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....","url_abs":"https://arxiv.org/abs/2507.07461","url_pdf":"https://arxiv.org/pdf/2507.07461v1","authors":"[\"Joshua Murphy\",\"Conor Rosato\",\"Andrew Millard\",\"Lee Devlin\",\"Paul Horridge\",\"Simon Maskell\"]","published":"2025-07-10T06:26:54Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.CO\"]","methods":"[\"LoRA\"]","has_code":false}