Christian Svensson presents his master's thesis

Bayesian Inference in General State Space Models using Sequential Monte 
Carlo Methods


Abstract:


In this thesis we use a sequential Monte Carlo-based Markov chain
Monte  Carlo sampler for estimating parameters in general state space
models. The  standard sequential Monte Carlo scheme, which suffers
from  particle  trajectory degeneracy when the number of observations
grows, is compared  to a robustified version proposed by Olsson
(2008). The idea of this  new scheme is to divide the state
trajectories into blocks, and by using a  forgetting property
possessed by a large class of state space models we  approximate the
smoothing density by running the algorithm blockwise. By  using this
scheme a bias is introduced but, with suitiable choise of the
introduced lag parameter the bias can be minimized. We apply the
algorithms to Bayesian inference in a linear Gaussian model and a
stochastic volatility model. In the latter, the algorithms are tested
against a pseudo-dominating Metropolis sampler proposed by  Pitt and
Shephard (1997), and the outcome of the simulation experiment  shows a
clear advantage for the block-sampler in terms of computational
complexity.