Second-order Particle MCMC for Bayesian Parameter Inference

We propose an improved proposal distribution in the Particle Metropolis-Hastings (PMH) algorithm for Bayesian parameter inference in nonlinear state space models (SSMs). This proposal incorporates second-order information about the posterior distribution over the system parameters, which can be extracted from the particle filter used in the PMH algorithm. This makes the algorithm scale-invariant, simpler to calibrate and shortens the burn-in phase. We also suggest improvements that reduces the computational complexity of our earlier first-order method. The complexity of the previous method is quadratic in the number of particles, whereas the new second-order method is linear.