Confidence intervals for finite difference solutions. Issue 7 (9th August 2018)

• Record Type: Journal Article
• Authors: John, Majnu; Wu, Yihren
• Is Part Of: Communications in statistics. Volume 47:Issue 7(2018)
• Page Start: 2102
• Page End: 2118
• Publication Date: 2018-08-09
• Subjects: Bayesian analysis -- Finite difference method -- Numerical analysis; 62P99 -- 65D25; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1335409
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it is only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework, we apply a simple Bayesian strategy to obtain confidence intervals for the finite difference solutions. We apply this framework on several examples to show how the confidence intervals are related to truncation error and illustrate the utility of the confidence intervals for the examples considered.