TY - JOUR

T1 - The Alive Particle Filter and Its Use in Particle Markov Chain Monte Carlo

AU - Moral, Pierre Del

AU - Jasra, Ajay

AU - Lee, Anthony

AU - Yau, Christopher

AU - Zhang, Xiaole

N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In the following article, we investigate a particle filter for approximating Feynman–Kac models with indicator potentials and we use this algorithm within Markov chain Monte Carlo (MCMC) to learn static parameters of the model. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rare-event problems. Such models require the use of advanced particle filter or MCMC algorithms to perform estimation. One of the drawbacks of existing particle filters is that they may “collapse,” in that the algorithm may terminate early, due to the indicator potentials. In this article, using a newly developed special case of the locally adaptive particle filter, we use an algorithm that can deal with this latter problem, while introducing a random cost per-time step. In particular, we show how this algorithm can be used within MCMC, using particle MCMC. It is established that, when not taking into account computational time, when the new MCMC algorithm is applied to a simplified model it has a lower asymptotic variance in comparison to a standard particle MCMC algorithm. Numerical examples are presented for ABC approximations of HMMs.

AB - In the following article, we investigate a particle filter for approximating Feynman–Kac models with indicator potentials and we use this algorithm within Markov chain Monte Carlo (MCMC) to learn static parameters of the model. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rare-event problems. Such models require the use of advanced particle filter or MCMC algorithms to perform estimation. One of the drawbacks of existing particle filters is that they may “collapse,” in that the algorithm may terminate early, due to the indicator potentials. In this article, using a newly developed special case of the locally adaptive particle filter, we use an algorithm that can deal with this latter problem, while introducing a random cost per-time step. In particular, we show how this algorithm can be used within MCMC, using particle MCMC. It is established that, when not taking into account computational time, when the new MCMC algorithm is applied to a simplified model it has a lower asymptotic variance in comparison to a standard particle MCMC algorithm. Numerical examples are presented for ABC approximations of HMMs.

UR - http://www.tandfonline.com/doi/full/10.1080/07362994.2015.1060892

UR - http://www.scopus.com/inward/record.url?scp=84944895637&partnerID=8YFLogxK

U2 - 10.1080/07362994.2015.1060892

DO - 10.1080/07362994.2015.1060892

M3 - Article

SN - 1532-9356

VL - 33

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 6

ER -