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Bayesian Projected Calibration of Computer Models

We develop a Bayesian approach called the Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the L2-projection constraint. The calibration parameter is estimated through its posterior distribution, serving as a natural and nonasymptotic approach for the uncertainty quantification. We provide rigorous large sample justifications of the proposed approach by establishing the asymptotic normality of the posterior of the calibration parameter with the efficient covariance matrix. In addition to the theoretical analysis, two convenient computational algorithms based on stochastic approximation are designed with strong theoretical support. Through extensive simulation studies and the analyses of two real-world datasets, we show that the proposed Bayesian projected calibration can accurately estimate the calibration parameters, calibrate the computer models well, and compare favorably to alternative approaches. Supplementary materials for this article are available online.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (JASA); Vol.116 No.536 December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1965-1982

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ASYMPTOTIC NORMALITY
UNCERTAINTY QUANTIFICATION
SEMIPARAMETRIC EFFICIENCY
COMPUTER EXPERIMENT
L2-PROJECTION

Info Detail Spesifik

https://doi.org/10.1080/01621459.2020.1753519

Pernyataan Tanggungjawab

Fangzheng Xie, Yanxun Xu

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