Approximating optimal smc proposal distributions in individual-based epidemic models

Many epidemic models are naturally defined as individual -based models, in which we track the state of each individual within a susceptible population. However, inference for individual -based models is challenging because of the highdimensional state -space of such models, which increases exponentially with the population size. Here, we consider sequential Monte Carlo algorithms for inference for individual -based epidemic models, where we make direct observations of the state of a sample of individuals. Standard implementations, such as the bootstrap filter and auxiliary particle filter, are inefficient, owing to a mismatch between the proposal distribution of the state and future observations. We develop new efficient proposal distributions that consider future observations, leveraging the following properties: (i) we can analytically calculate the optimal proposal distribution for a single individual, given future observations and the future infection rate of that individual; and (ii) the dynamics of individuals are independent if we condition on their infection rates. Thus, we construct estimates of the future infection rate for each individual, and then use an independent proposal for the state of each individual, given this estimate. Empirical results show orders of magnitude improvement in efficiency of the sequential Monte Carlo sampler for both SIS and SEIR models.