Multi-index sequential monte carlo methods for partially observed stochastic partial differential equations

Ajay Jasra; Kody J.H. Law; Yaxian Xu

doi:10.1615/Int.J.UncertaintyQuantification.2020033219

Multi-index sequential monte carlo methods for partially observed stochastic partial differential equations

Ajay Jasra, Kody J.H. Law, Yaxian Xu

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation. It is assumed that one can only estimate the hidden state using a discretization of the model. In this context, it is known that the multi-index Monte Carlo (MIMC) method can be used to improve over direct Monte Carlo from the most precise discretizaton. However, in the context of interest, it cannot be directly applied, but rather must be used within another method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the standard identity and approximating the resulting identity using the SMC2 method, which is an exact method that can be used in this context. We prove that our approach can reduce the cost to obtain a given mean square error, relative to just using SMC2 on the most precise discretization. We demonstrate this with some numerical examples.

Original language	English (US)
Pages (from-to)	1-25
Number of pages	25
Journal	International Journal for Uncertainty Quantification
Volume	11
Issue number	3
DOIs	https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020033219
State	Published - 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-04-22
Acknowledged KAUST grant number(s): CRG4 grant ref: 2584
Acknowledgements: We would like to thank Abdul-Lateef Haji-Ali for useful discussions relating to the material in this paper. A.J. was supported by a KAUST CRG4 grant ref: 2584 and KAUST baseline funding. K.J.H.L. and A.J. were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), under field work proposal number ERKJ333. K.J.H.L. was additionally supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. He was also funded in part by Oak Ridge National Laboratory Directed Research and Development Seed funding.

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Discrete Mathematics and Combinatorics
Control and Optimization

Access to Document

10.1615/Int.J.UncertaintyQuantification.2020033219

https://repository.kaust.edu.sa/bitstream/10754/661011/4/1805.00415.pdf

Cite this

@article{7e78aeb543184c13984f4b102230a282,

title = "Multi-index sequential monte carlo methods for partially observed stochastic partial differential equations",

abstract = "In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation. It is assumed that one can only estimate the hidden state using a discretization of the model. In this context, it is known that the multi-index Monte Carlo (MIMC) method can be used to improve over direct Monte Carlo from the most precise discretizaton. However, in the context of interest, it cannot be directly applied, but rather must be used within another method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the standard identity and approximating the resulting identity using the SMC2 method, which is an exact method that can be used in this context. We prove that our approach can reduce the cost to obtain a given mean square error, relative to just using SMC2 on the most precise discretization. We demonstrate this with some numerical examples.",

author = "Ajay Jasra and Law, {Kody J.H.} and Yaxian Xu",

note = "KAUST Repository Item: Exported on 2021-04-22 Acknowledged KAUST grant number(s): CRG4 grant ref: 2584 Acknowledgements: We would like to thank Abdul-Lateef Haji-Ali for useful discussions relating to the material in this paper. A.J. was supported by a KAUST CRG4 grant ref: 2584 and KAUST baseline funding. K.J.H.L. and A.J. were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), under field work proposal number ERKJ333. K.J.H.L. was additionally supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. He was also funded in part by Oak Ridge National Laboratory Directed Research and Development Seed funding.",

year = "2021",

doi = "10.1615/Int.J.UncertaintyQuantification.2020033219",

language = "English (US)",

volume = "11",

pages = "1--25",

journal = "International Journal for Uncertainty Quantification",

issn = "2152-5099",

publisher = "Begell House Inc.",

number = "3",

}

TY - JOUR

T1 - Multi-index sequential monte carlo methods for partially observed stochastic partial differential equations

AU - Jasra, Ajay

AU - Law, Kody J.H.

AU - Xu, Yaxian

N1 - KAUST Repository Item: Exported on 2021-04-22 Acknowledged KAUST grant number(s): CRG4 grant ref: 2584 Acknowledgements: We would like to thank Abdul-Lateef Haji-Ali for useful discussions relating to the material in this paper. A.J. was supported by a KAUST CRG4 grant ref: 2584 and KAUST baseline funding. K.J.H.L. and A.J. were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), under field work proposal number ERKJ333. K.J.H.L. was additionally supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. He was also funded in part by Oak Ridge National Laboratory Directed Research and Development Seed funding.

PY - 2021

Y1 - 2021

N2 - In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation. It is assumed that one can only estimate the hidden state using a discretization of the model. In this context, it is known that the multi-index Monte Carlo (MIMC) method can be used to improve over direct Monte Carlo from the most precise discretizaton. However, in the context of interest, it cannot be directly applied, but rather must be used within another method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the standard identity and approximating the resulting identity using the SMC2 method, which is an exact method that can be used in this context. We prove that our approach can reduce the cost to obtain a given mean square error, relative to just using SMC2 on the most precise discretization. We demonstrate this with some numerical examples.

AB - In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation. It is assumed that one can only estimate the hidden state using a discretization of the model. In this context, it is known that the multi-index Monte Carlo (MIMC) method can be used to improve over direct Monte Carlo from the most precise discretizaton. However, in the context of interest, it cannot be directly applied, but rather must be used within another method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the standard identity and approximating the resulting identity using the SMC2 method, which is an exact method that can be used in this context. We prove that our approach can reduce the cost to obtain a given mean square error, relative to just using SMC2 on the most precise discretization. We demonstrate this with some numerical examples.

UR - http://hdl.handle.net/10754/661011

UR - http://www.dl.begellhouse.com/journals/52034eb04b657aea,6849ac9f50c363c1,3c52cac35ff03994.html

UR - http://www.scopus.com/inward/record.url?scp=85103982223&partnerID=8YFLogxK

U2 - 10.1615/Int.J.UncertaintyQuantification.2020033219

DO - 10.1615/Int.J.UncertaintyQuantification.2020033219

M3 - Article

SN - 2152-5099

VL - 11

SP - 1

EP - 25

JO - International Journal for Uncertainty Quantification

JF - International Journal for Uncertainty Quantification

IS - 3

ER -

Multi-index sequential monte carlo methods for partially observed stochastic partial differential equations

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this