Auxiliary Particle filtering within adaptive Metropolis-Hastings Sampling

Understand

Our article deals with Bayesian inference for a general state space model with the simulated likelihood computed by the particle filter.

• We show empirically that the partially or fully adapted particle filters can be much more efficient than the standard particle, especially when the signal to noise ratio is high.
• This is especially important because using the particle filter within MCMC sampling is O(T^2), where T is the sample size.
• We also show that an adaptive independent proposal for the unknown parameters based on a mixture of normals can be much more efficient than the usual optimal random walk methods because the simulated likelihood is not continuous in the parameters and the cost of constructing a good adaptive proposal is negligible compared to the cost of evaluating the simulated likelihood.