Sequential Monte Carlo (SMC) methods are widely used in State-Space Models (SSMs) to sample particles from and marginalise over underlying latent processes. Common SMC challenges, such as particle degradation, are exacerbated when the latent process evolves on discrete bounded domains: proposed particles may be incompatible with the data, lying in low-probability regions or outside the boundary constraints, and the system could result in all particles having 0-weights (i.e. particle collapse). In this talk, I will present the Lifebelt Particle Filter (LBPF), a robust SMC method for likelihood estimation, and demonstrate its application to estimating f the severity of an emerging epidemic. The LBPF combines a standard particle filter with one (or more) lifebelt particles, which, by construction, lie within the boundaries of the latent process and therefore are compatible with the data, protecting against full particle collapse.
I will conclude by showing how the principles underlying the LBPF can be extended to develop a general class of collapse-proof SMC schemes.
This is joint work with Simon Spencer and Richard Haughey.