Wentao Li (Lancaster University): Efficient Sequential Monte Carlo with Multiple Proposals and Control Variates

Sequential Monte Carlo is a useful method for online filtering of state space models. Due to the complexity of modern problems, a single proposal distribution is usually not efficient and considering multiple proposal distributions is a general method to address various as- pects of the filtering. This paper proposes an efficient method of using multiple proposals in combination with control variates. Tan (2004)’s likelihood approach is used in both resam- pling and estimation. The new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates. The guidance for selecting multiple proposals and control variates is also given. Numerical studies of the AR(1) model observed with noise and the stochastic volatility model with AR(1) dynamics show that the new algo- rithm can significantly improve over the bootstrap filter and auxiliary particle filter.