publication . Article . Preprint . 2015

sequential monte carlo with highly informative observations

Moral, Pierre Del; Lawrence Murray;
Open Access
  • Published: 01 Jan 2015 Journal: SIAM/ASA Journal on Uncertainty Quantification, volume 3, pages 969-997 (eissn: 2166-2525, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
  • Country: United Kingdom
Abstract
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is simulating bridges between given initial and final values. The basic idea is to introduce a schedule of intermediate weighting and resampling times between observation times, which guide particles towards the final state. This can always be done for continuous-time models, and may be done for discrete-time models under sparse observation regimes; our main focus is on continuous-time diffusion processes. The methods are broadly app...
Subjects
free text keywords: Weighting, Bayesian statistics, Algorithm, Approximate Bayesian computation, Pointwise, Posterior probability, Particle filter, Mathematics, Sampling (statistics), Resampling, Mathematical optimization, Statistics - Computation, Statistics - Applications, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Related Organizations
39 references, page 1 of 3

C. Andrieu, A. Doucet, and R. Holenstein. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society Series B, 72:269-302, 2010.

Anonymous. Influenza in a boarding school. British Medical Journal, 1:587, March 1978. URL http: //www.ncbi.nlm.nih.gov/pmc/articles/PMC1603269/?page=2.

Y. Aït-Sahalia. Transition densities for interest rate and other nonlinear diffusions. The Journal of Finance, 54(4):1361-1395, 1999. ISSN 1540-6261. doi: 10.1111/0022-1082.00149. [OpenAIRE]

C. Bayer and J. Schoenmakers. Simulation of forward-reverse stochastic representations for conditional diffusions. 2013. URL http://arxiv.org/abs/1306.2452. [OpenAIRE]

M. A. Beaumont, W. Zhang, and D. J. Balding. Approximate Bayesian computation in population genetics. Genetics, 162:2025-2035, 2002. [OpenAIRE]

M. A. Beaumont, J.-M. Cornuet, J.-M. Marin, and C. P. Robert. Adaptive approximate Bayesian computation. Biometrika, 96(4):983-990, 2009. doi: 10.1093/biomet/asp052.

A. Beskos, O. Papaspiliopoulos, G. Roberts, and P. Fearnhead. Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. Journal of the Royal Statistical Society Series B, 68:333-382, 2006. [OpenAIRE]

M. H. Carpenter and C. A. Kennedy. Fourth-order 2N-storage Runge-Kutta schemes. Technical Report Technical Memorandum 109112, National Aeronautics and Space Administration, June 1994.

N. Chopin, P. Jacob, and O. Papaspiliopoulos. SMC2: An efficient algorithm for sequential analysis of state space models. Journal of the Royal Statistical Society B, 75, 2012. doi: 10.1111/j.1467-9868. 2012.01046.x.

J. Clark. The simulation of pinned diffusions. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 1418-1420. IEEE, 1990.

P. Del Moral, A. Doucet, and A. Jasra. An adaptive sequential Monte Carlo method for approximate Bayesian computation. Statistics and Computing, 22:1009-1020, 2012. doi: 10.1007/ s11222-011-9271-y.

B. Delyon and Y. Hu. Simulation of conditioned diffusion and application to parameter estimation. Stochastic Processes and their Applications, 116(11):1660 - 1675, 2006. ISSN 0304-4149. doi: 10.1016/ j.spa.2006.04.004. [OpenAIRE]

G. B. Durham and A. R. Gallant. Numerical techniques for maximum likelihood estimation of continuoustime diffusion processes. Journal of Business and Economic Statistics, 20(3):297-316, 2002.

O. Elerian, S. Chib, and N. Shephard. Likelihood inference for discretely observed nonlinear diffusions. Econometrica, 69(4):959-993, 2001. ISSN 00129682. [OpenAIRE]

B. Eraker. MCMC analysis of diffusion models with application to finance. Journal of Business & Economic Statistics, 19(2):177-191, 2001. doi: 10.1198/073500101316970403. [OpenAIRE]

39 references, page 1 of 3
Abstract
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is simulating bridges between given initial and final values. The basic idea is to introduce a schedule of intermediate weighting and resampling times between observation times, which guide particles towards the final state. This can always be done for continuous-time models, and may be done for discrete-time models under sparse observation regimes; our main focus is on continuous-time diffusion processes. The methods are broadly app...
Subjects
free text keywords: Weighting, Bayesian statistics, Algorithm, Approximate Bayesian computation, Pointwise, Posterior probability, Particle filter, Mathematics, Sampling (statistics), Resampling, Mathematical optimization, Statistics - Computation, Statistics - Applications, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Related Organizations
39 references, page 1 of 3

C. Andrieu, A. Doucet, and R. Holenstein. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society Series B, 72:269-302, 2010.

Anonymous. Influenza in a boarding school. British Medical Journal, 1:587, March 1978. URL http: //www.ncbi.nlm.nih.gov/pmc/articles/PMC1603269/?page=2.

Y. Aït-Sahalia. Transition densities for interest rate and other nonlinear diffusions. The Journal of Finance, 54(4):1361-1395, 1999. ISSN 1540-6261. doi: 10.1111/0022-1082.00149. [OpenAIRE]

C. Bayer and J. Schoenmakers. Simulation of forward-reverse stochastic representations for conditional diffusions. 2013. URL http://arxiv.org/abs/1306.2452. [OpenAIRE]

M. A. Beaumont, W. Zhang, and D. J. Balding. Approximate Bayesian computation in population genetics. Genetics, 162:2025-2035, 2002. [OpenAIRE]

M. A. Beaumont, J.-M. Cornuet, J.-M. Marin, and C. P. Robert. Adaptive approximate Bayesian computation. Biometrika, 96(4):983-990, 2009. doi: 10.1093/biomet/asp052.

A. Beskos, O. Papaspiliopoulos, G. Roberts, and P. Fearnhead. Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. Journal of the Royal Statistical Society Series B, 68:333-382, 2006. [OpenAIRE]

M. H. Carpenter and C. A. Kennedy. Fourth-order 2N-storage Runge-Kutta schemes. Technical Report Technical Memorandum 109112, National Aeronautics and Space Administration, June 1994.

N. Chopin, P. Jacob, and O. Papaspiliopoulos. SMC2: An efficient algorithm for sequential analysis of state space models. Journal of the Royal Statistical Society B, 75, 2012. doi: 10.1111/j.1467-9868. 2012.01046.x.

J. Clark. The simulation of pinned diffusions. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 1418-1420. IEEE, 1990.

P. Del Moral, A. Doucet, and A. Jasra. An adaptive sequential Monte Carlo method for approximate Bayesian computation. Statistics and Computing, 22:1009-1020, 2012. doi: 10.1007/ s11222-011-9271-y.

B. Delyon and Y. Hu. Simulation of conditioned diffusion and application to parameter estimation. Stochastic Processes and their Applications, 116(11):1660 - 1675, 2006. ISSN 0304-4149. doi: 10.1016/ j.spa.2006.04.004. [OpenAIRE]

G. B. Durham and A. R. Gallant. Numerical techniques for maximum likelihood estimation of continuoustime diffusion processes. Journal of Business and Economic Statistics, 20(3):297-316, 2002.

O. Elerian, S. Chib, and N. Shephard. Likelihood inference for discretely observed nonlinear diffusions. Econometrica, 69(4):959-993, 2001. ISSN 00129682. [OpenAIRE]

B. Eraker. MCMC analysis of diffusion models with application to finance. Journal of Business & Economic Statistics, 19(2):177-191, 2001. doi: 10.1198/073500101316970403. [OpenAIRE]

39 references, page 1 of 3
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publication . Article . Preprint . 2015

sequential monte carlo with highly informative observations

Moral, Pierre Del; Lawrence Murray;