Abstract: Particle filters, also known as sequential Monte Carlo, are a powerful computational tool for making inference with dynamical systems. In particular, it is widely used in state space models to estimate the likelihood function. However, estimating the gradient of the likelihood function is hard with sequential Monte Carlo, partially because the commonly used reparametrization trick is not applicable due to the discrete nature of the resampling step. To address this problem, we propose utilizing the smoothly jittered particle filter, which smooths the discrete resampling by adding noise to the resampled particles. We show that when the noise level is chosen correctly, no additional asymptotic error is introduced to the resampling step. We support our method with simulations.

Key words and phrases: Reparametrization trick, resampling, sequential Monte Carlo, state space models.