Abstract

Sequential Monte Carlo (SMC) methods can be applied to discrete State-Space Models on bounded domains, to sample from and marginalise over unknown random variables. Similarly to continuous settings, problems such as particle degradation can arise: proposed particles can be incompatible with the data, lying in low probability regions or outside the boundary constraints, and the discrete system could result in all particles having weights of zero. In this talk I will introduce the Lifebelt Particle Filter (LBPF), a novel SMC method for robust likelihood estimation in low-valued count problems. The LBPF combines a standard particle filter with one (or more) lifebelt particles which, by construction, lie within the boundaries of the discrete random variables, and therefore are compatible with the data. The main benefit of the LBPF is that only one or few, wisely chosen, particles are sufficient to prevent particle collapse. The LBPF can be used within a pseudo-marginal scheme to draw inferences on static parameters, θ, governing the system. In the talk I will also present an example of the use of the LBPF for the estimation of the parameters governing the death and recovery process of hospitalised patients during an epidemic.