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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Bayesian regression versus application of least squares—an example
Author(s): C. Elster and G. Wübbeler
Journal: Metrologia
Year: 2016
Volume: 53
Issue: 1
Pages: S10
DOI: 10.1088/0026-1394/53/1/S10
Web URL: http://stacks.iop.org/0026-1394/53/i=1/a=S10
Tags: 8.4, 8.42, Unsicherheit, Regression
Abstract: Regression is an important task in metrology and least-squares methods are often applied in this context. Bayesian inference provides an alternative that can take into account available prior knowledge. We illustrate similarities and differences of the two approaches in terms of a particular nonlinear regression problem. The impact of prior knowledge utilized in the Bayesian regression depends on the amount of information contained in the data, and by considering data sets with different signal-to-noise ratios the relevance of the employed prior knowledge for the results is investigated. In addition, properties of the two approaches are explored in the context of the particular example.

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