%0 Journal Article %1 middleton2019unbiased %A Middleton, Lawrence %A Deligiannidis, George %A Doucet, Arnaud %A Jacob, Pierre E. %D 2019 %K bayesian mcmc %T Unbiased Smoothing using Particle Independent Metropolis-Hastings %U http://arxiv.org/abs/1902.01781 %X We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévy-driven stochastic volatility model and a stochastic kinetic model.

@article{middleton2019unbiased, abstract = {We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a L\'evy-driven stochastic volatility model and a stochastic kinetic model.}, added-at = {2019-03-02T23:08:30.000+0100}, author = {Middleton, Lawrence and Deligiannidis, George and Doucet, Arnaud and Jacob, Pierre E.}, biburl = {https://www.bibsonomy.org/bibtex/239c5cf41be90b757d2d85732cb0c78d1/kirk86}, description = {[1902.01781] Unbiased Smoothing using Particle Independent Metropolis-Hastings}, interhash = {a52fe9e2bcc80cceb214bf48108ec8ea}, intrahash = {39c5cf41be90b757d2d85732cb0c78d1}, keywords = {bayesian mcmc}, note = {cite arxiv:1902.01781Comment: 13 pages}, timestamp = {2019-03-02T23:08:30.000+0100}, title = {Unbiased Smoothing using Particle Independent Metropolis-Hastings}, url = {http://arxiv.org/abs/1902.01781}, year = 2019 }