Dimension reduction in statistical estimation of partially observed multiscale processes

Andrew Papanicolaou; Konstantinos Spiliopoulos

doi:10.1137/16M1085930

Dimension reduction in statistical estimation of partially observed multiscale processes

Andrew Papanicolaou, Konstantinos Spiliopoulos

Finance and Risk Engineering

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

Abstract

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows us to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.

Original language	English (US)
Pages (from-to)	1220-1247
Number of pages	28
Journal	SIAM-ASA Journal on Uncertainty Quantification
Volume	5
Issue number	1
DOIs	https://doi.org/10.1137/16M1085930
State	Published - 2017

Keywords

Data assimilation
Dimension reduction
Filtering
Homogenization
Multiscale diffusions
Parameter estimation

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Statistics, Probability and Uncertainty
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1137/16M1085930

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abstract = "We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows us to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.",

keywords = "Data assimilation, Dimension reduction, Filtering, Homogenization, Multiscale diffusions, Parameter estimation",

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AU - Spiliopoulos, Konstantinos

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AB - We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows us to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.

KW - Data assimilation

KW - Dimension reduction

KW - Filtering

KW - Homogenization

KW - Multiscale diffusions

KW - Parameter estimation

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JF - SIAM-ASA Journal on Uncertainty Quantification

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Dimension reduction in statistical estimation of partially observed multiscale processes

Abstract

Keywords

ASJC Scopus subject areas

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