Hi, I have another question regarding the particle filter and estimation. When estimating particle filter, log-likelihood tend to be erratic due to intrinsic randomness in particles. For that reason, you suggest to use metropolis Hastings or optimisation algorithms without gradient estimation. I was wondering if you happen to know whether using prior in addition to likelihood makes sure that the posterior is smoother and, therefore, reducing problems with the non-smooth log likelihood?
No, the likelihood is discontinuous. Adding a smoother function (prior) to a discontinuous one does not remove them.