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Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo

Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated from noisy measurements of the dynamic system. Generally, there is no closed-form solution for nonlinear DEs, and the likelihood surface for the parameter of interest is multi-modal and very sensitive to different parameter values. We propose a Bayesian framework for nonlinear DE systems. A flexible nonparametric function is used to represent the dynamic process such that expensive numerical solvers can be avoided. A sequential Monte Carlo algorithm in the annealing framework is proposed to conduct Bayesian inference for parameters in DEs. In our numerical experiments, we use examples of ordinary differential equations and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We developed an R package that is available at https://github.com/shijiaw/smcDE. Supplementary files for this article are available online.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS; Vol.31 No.2 June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 600-613

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

DELAY DIFFERENTIAL EQUATION
B-SPLINE
ORDINARY DIFFERENTIAL EQUATION
BAYESIAN SMOOTHING
CONDITIONAL EFFECTIVE SAMPLE SIZE

Info Detail Spesifik

https://doi.org/10.1080/10618600.2021.1987252

Pernyataan Tanggungjawab

Shijia Wang, Shufei Ge, Renny Doig, Liangliang Wang

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