Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo

Jasra, Ajay; Kamatani, Kengo; Law, Kody; Zhou, Yan

doi:10.1137/17m1112595

Title: Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo

Journal Article · Tue Mar 27 00:00:00 EDT 2018 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/17m1112595· OSTI ID:1862173

Jasra, Ajay ^[1]; Kamatani, Kengo ^[2];

^[3]; Zhou, Yan ^[1]

National Univ. of Singapore (Singapore)
Osaka Univ. (Japan)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method. Given this assumption, we show how one can use Markov chain Monte Carlo (MCMC) and particularly particle MCMC [C. Andrieu, A. Doucet, and R. Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 72 (2010), 269--342] to implement a new approximation of the multilevel (ML) Monte Carlo (MC) collapsing sum identity. Our approach comprises constructing an approximate coupling of the posterior density of the joint distribution over parameter and hidden variables at two different discretization levels and then correcting by an importance sampling method. The variance of the weights are independent of the length of the observed data set. The utility of such a method is that, for a prescribed level of mean square error, the cost of this MLMC method is provably less than i.i.d. sampling from the posterior associated to the most precise discretization. However the method here comprises using only known and efficient simulation methodologies. Finally, the theoretical results are illustrated by inference of the parameters of two prototypical processes given noisy partial observations of the process: the first is an Ornstein--Uhlenbeck process and the second is a more general Langevin equation.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1862173

Journal Information:: SIAM Journal on Scientific Computing, Vol. 40, Issue 2; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

References (12)

Multilevel Monte Carlo Path Simulation Giles, Michael B. Operations Research, Vol. 56, Issue 3 https://doi.org/10.1287/opre.1070.0496	journal	June 2008
Particle Markov chain Monte Carlo methods: Particle Markov Chain Monte Carlo Methods Andrieu, Christophe; Doucet, Arnaud; Holenstein, Roman Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 72, Issue 3 https://doi.org/10.1111/j.1467-9868.2009.00736.x	journal	June 2010
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients Cliffe, K. A.; Giles, M. B.; Scheichl, R. Computing and Visualization in Science, Vol. 14, Issue 1 https://doi.org/10.1007/s00791-011-0160-x	journal	January 2011
Complexity analysis of accelerated MCMC methods for Bayesian inversion Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. Inverse Problems, Vol. 29, Issue 8 https://doi.org/10.1088/0266-5611/29/8/085010	journal	July 2013
A Liapounov bound for solutions of the Poisson equation Glynn, Peter W.; Meyn, Sean P. The Annals of Probability, Vol. 24, Issue 2 https://doi.org/10.1214/aop/1039639370	journal	April 1996
On coupling particle filter trajectories Sen, Deborshee; Thiery, Alexandre H.; Jasra, Ajay Statistics and Computing, Vol. 28, Issue 2 https://doi.org/10.1007/s11222-017-9740-z	journal	March 2017
Multilevel particle filters: normalizing constant estimation Jasra, Ajay; Kamatani, Kengo; Osei, Prince Peprah Statistics and Computing, Vol. 28, Issue 1 https://doi.org/10.1007/s11222-016-9715-5	journal	November 2016
A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow Dodwell, T. J.; Ketelsen, C.; Scheichl, R. SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, Issue 1 https://doi.org/10.1137/130915005	journal	January 2015
Geometric Ergodicity and Hybrid Markov Chains Roberts, Gareth; Rosenthal, Jeffrey Electronic Communications in Probability, Vol. 2, Issue none https://doi.org/10.1214/ECP.v2-981	journal	January 1997
The correlated pseudomarginal method Deligiannidis, George; Doucet, Arnaud; Pitt, Michael K. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 80, Issue 5 https://doi.org/10.1111/rssb.12280	journal	July 2018
A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow Dodwell, T. J.; Ketelsen, C.; Scheichl, R. arXiv https://doi.org/10.48550/arxiv.1303.7343	preprint	January 2013
Coupling of Particle Filters Jacob, Pierre E.; Lindsten, Fredrik; Schön, Thomas B. arXiv https://doi.org/10.48550/arxiv.1606.01156	preprint	January 2016

Cited By (7)

Multilevel Monte Carlo in approximate Bayesian computation Jasra, Ajay; Jo, Seongil; Nott, David Stochastic Analysis and Applications, Vol. 37, Issue 3 https://doi.org/10.1080/07362994.2019.1566006	journal	January 2019
Multilevel Monte Carlo in Approximate Bayesian Computation Jasra, Ajay; Jo, Seongil; Nott, David arXiv https://doi.org/10.48550/arxiv.1702.03628	preprint	January 2017
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art Warne, David J.; Baker, Ruth E.; Simpson, Matthew J. arXiv https://doi.org/10.48550/arxiv.1812.05759	text	January 2018
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art Warne, David J.; Baker, Ruth E.; Simpson, Matthew J. Journal of The Royal Society Interface, Vol. 16, Issue 151 https://doi.org/10.1098/rsif.2018.0943	journal	February 2019
Multi-Index Sequential Monte Carlo Methods for Partially Observed Stochastic Partial Differential Equations Jasra, Ajay; Law, Kody J. H.; Xu, Yaxian International Journal for Uncertainty Quantification, Vol. 11, Issue 3 https://doi.org/10.1615/int.j.uncertaintyquantification.2020033219	journal	January 2021
A Multi-Index Markov Chain Monte Carlo Method Jasra, Ajay; Kamatani, Kengo; Law, Kody arXiv https://doi.org/10.48550/arxiv.1704.00117	preprint	January 2017
Advanced Multilevel Monte Carlo Methods Jasra, Ajay; Law, Kody; Suciu, Carina arXiv https://doi.org/10.48550/arxiv.1704.07272	preprint	January 2017

Similar Records

Multilevel sequential Monte Carlo samplers

Journal Article · Wed Aug 24 00:00:00 EDT 2016 · Stochastic Processes and Their Applications · OSTI ID:1862173

Beskos, Alexandros; Jasra, Ajay; Law, Kody; +2 more

Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

Journal Article · Fri Jan 01 00:00:00 EST 2016 · International Journal for Uncertainty Quantification · OSTI ID:1862173

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

Advanced Multilevel Monte Carlo Methods

Journal Article · Tue Mar 03 00:00:00 EST 2020 · International Statistical Review · OSTI ID:1862173

Jasra, Ajay; Law, Kody; Suciu, Carina

Related Subjects

97 MATHEMATICS AND COMPUTING
multilevel Monte Carlo
Markov chain Monte Carlo
diffusion processes

Title: Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo

Citation Formats

References (12)

Cited By (7)

Similar Records

Related Subjects