Parameter estimation in Conditional Sequential Monte Carlo algorithms through Particle Learning

In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to Gibbs sampling in settings where strong internal correlations may challenge effective exploration. We include an application to the estimation of weights in a branching process model against synthetic data and show that, in this setting, performance is dramatically enhanced, with substantially faster mixing and markedly reduced autocorrelation compared with standard particle Gibbs implementations.