Fearnhead, Paul; Papaspiliopoulos, Omiros; Roberts, Gareth O.; Stuart, Andrew Random-weight particle filtering of continuous time processes. (English) Zbl 1411.60109 J. R. Stat. Soc., Ser. B, Stat. Methodol. 72, No. 4, 497-512 (2010). Summary: It is possible to implement importance sampling, and particle filter algorithms, where the importance sampling weight is random. Such random-weight algorithms have been shown to be efficient for inference for a class of diffusion models, as they enable inference without any (time discretization) approximation of the underlying diffusion model. One difficulty of implementing such random-weight algorithms is the requirement to have weights that are positive with probability 1. We show how Wald’s identity for martingales can be used to ensure positive weights. We apply this idea to analysis of diffusion models from high frequency data. For a class of diffusion models we show how to implement a particle filter, which uses all the information in the data, but whose computational cost is independent of the frequency of the data. We use the Wald identity to implement a random-weight particle filter for these models which avoids time discretization error. Cited in 12 Documents MSC: 60J22 Computational methods in Markov chains 65C40 Numerical analysis or methods applied to Markov chains 62M20 Inference from stochastic processes and prediction Keywords:diffusions; exact simulation; Gaussian process; integrated processes; negative importance weights; Poisson estimator; sequential Monte Carlo methods PDFBibTeX XMLCite \textit{P. Fearnhead} et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 72, No. 4, 497--512 (2010; Zbl 1411.60109) Full Text: DOI