Sequential Monte Carlo Squared (SMC$^2$) method is designed to improve accuracy and computational efficiency in Bayesian inference.
The incorporation of second-order proposals, utilizing Hessian information, within SMC$^2$ framework enhances exploration of the posterior distribution.
Experimental results on synthetic models show the advantages of using second-order proposals in terms of step-size selection and posterior approximation accuracy.
This study extends the Metropolis-Adjusted Langevin Algorithm (MALA) by incorporating second-order information for better exploration of probability regions.